Bin Wang, Xinyun Zhu
In this paper, we study Whittaker modules for a Lie algebras of Block type. We define Whittaker modules and under some conditions, obtain a one to one correspondence between the set of isomorphic classes of Whittaker modules over this algebra and the set of ideals of a polynomial ring, parallel to a result from the classical setting and the case of the Virasoro algebra.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Following analogous constructions for Lie algebras, we define Whittaker modules and Whittaker categories for finite-dimensional simple Lie superalgebras. Results include a decomposition of Whittaker categories for a Lie superalgebra according to the action of an appropriate sub-superalgebra; and, for basic classical Lie superalgebras of type I, a description of the strongly typical simple Whittaker modules.
In this paper, we study Whittaker modules for graded Lie algebras. We define Whittaker modules for a class of graded Lie algebras and obtain a bijective correspondence between the set of isomorphism classes of Whittaker modules and the set of ideals of a polynomial ring, parallel to a result from the classical setting and the case of the Virasoro algebra. As a consequence of this, we obtain a classification of simple Whittaker modules for such algebras. Also, we study some concrete algebras as examples.
We classify simple Whittaker modules for classical Lie superalgebras in terms of their parabolic decompositions. We establish a type of Miličić-Soergel equivalence of a category of Whittaker modules and a category of Harish-Chandra bimodules. For classical Lie superalgebras of type I, we reduce the problem of composition factors of standard Whittaker modules to that of Verma modules in their BGG categories $\mathcal O$. As a consequence, the composition series of standard Whittaker modules over the general linear Lie superalgebras $\mathfrak{gl}(m|n)$ and the ortho-symplectic Lie superalgebras…
Let $\mathcal{L}$ be the derivation Lie algebra of ${\mathbb C}[t_1^{\pm 1},t_2^{\pm 1}]$. Given a triangle decomposition $\mathcal{L} =\mathcal{L}^{+}\oplus\mathfrak{h}\oplus\mathcal{L}^{-}$, we define a nonsingular Lie algebra homomorphism $ψ:\mathcal{L}^{+}\rightarrow\mathbb{C}$ and the universal Whittaker $\mathcal{L}$-module $W_ψ$ of type $ψ$. We obtain all Whittaker vectors and submodules of $W_ψ$, and all simple Whittaker $\mathcal{L}$-modules of type $ψ$.
The Whittaker module $M_ψ$ and its quotient Whittaker module $L_{ψ, ξ}$ for the twisted affine Nappi-Witten Lie algebra $\widehat{H}_{4}[τ]$ are studied. For nonsingular type, it is proved that if $ξ\neq 0$, then $L_{ψ,ξ}$ is irreducible and any irreducible Whittaker $\widehat{H}_{4}[τ]$-module of type $ψ$ with ${\bf k}$ acting as a non-zero scalar $ξ$ is isomorphic to $L_{ψ,ξ}$. Furthermore, for $ξ=0$, all Whittaker vectors of $L_{ψ, 0}$ are completely determined. For singular type, the Whittaker vectors of $L_{ψ, ξ}$ with $ξ\neq 0$ are fully characterized.
This paper addresses the representation theory of the insertion-elimination Lie algebra, a Lie algebra that can be naturally realized in terms of tree-inserting and tree-eliminating operations on rooted trees. The insertion-elimination algebra admits a triangular decomposition in the sense of Moody and Pianzola, and thus it is natural to define a Whittaker module corresponding to a given algebra homomorphism. Among other results, we show that the standard Whittaker module is simple given certain constraints on the corresponding algebra homomorphism.
Inspired by recent activities on Whittaker modules over various (Lie) algebras we describe some general framework for the study of Lie algebra modules locally finite over a subalgebra. As a special case we obtain a very general setup for the study of Whittaker modules, which includes, in particular, Lie algebras with triangular decomposition and simple Lie algebras of Cartan type. We describe some basic properties of Whittaker modules, including a block decomposition of the category of Whittaker modules and certain properties of simple Whittaker modules under some rather mild assumptions. We e…
We extend Kostant's result on annihilator ideals of non-singular simple Whittaker modules over Lie algebras to (possibly singular) simple Whittaker modules over Lie superalgebras. We describe these annihilator ideals in terms of certain primitive ideals coming from the category $\mathcal O$ for quasireductive Lie superalgebras. To determine these annihilator ideals, we develop annihilator-preserving equivalences between certain full subcategories of the Whittaker category $\tilde{\mathcal N}$ and the categories of certain projectively presentable modules in the category $\mathcal O$. These equ…
Quasi-Whittaker supermodules over Lie superalgebras
本文发展了李超代数上拟Whittaker超模的一般理论，确定了拟Whittaker向量、建立不可约性判据并分类不可约超模，应用于多个超代数。
We use induction from parabolic subalgebras with infinite-dimensional Levi factor to construct new families of irreducible representations for arbitrary Affine Kac-Moody algebra. Our first construction defines a functor from the category of Whittaker modules over the Levi factor of a parabolic subalgebra to the category of modules over the Affine Lie algebra. The second functor sends tensor products of a module over the affine part of the Levi factor (in particular any weight module) and of a Whittaker module over the complement Heisenberg subalgebra to the Affine Lie algebra modules. Both fun…
Kostant's problem for Whittaker modules
本文研究 Lie 代数与 Lie 超代数上 Whittaker 模块的 Kostant 问题，给出 reductive Lie 代数上的充分条件，并发展归约结果将 I 型 Lie 超代数的问题归约至其偶部分。
We propose integral representations of the Whittaker functions for the classical Lie algebras sp(2l), so(2l) and so(2l+1). These integral representations generalize the integral representation of gl(l+1)-Whittaker functions first introduced by Givental. One of the salient features of the Givental representation is its recursive structure with respect to the rank of the Lie algebra gl(l+1). The proposed generalization of the Givental representation to the classical Lie algebras retains this property. It was shown elsewhere that the integral recursion operator for gl(l+1)-Whittaker function in t…
We show that, for an arbitrary quasi-reductive Lie superalgebra with a triangular decomposition and a character $ζ$ of the nilpotent radical, the associated Backelin functor $Γ_ζ$ sends Verma modules to standard Whittaker modules provided the latter exist. As a consequence, this gives a complete solution to the problem of determining the composition factors of the standard Whittaker modules in terms of composition factors of Verma modules in the category $\mathcal O$. In the case of the ortho-symplectic Lie superalgebras, we show that the Backelin functor $Γ_ζ$ and its target category, respect…
Whittaker modules have been well studied in the setting of complex semisimple Lie algebras. Their definition can easily be generalized to certain other Lie algebras with triangular decomposition, including the Virasoro algebra. We define Whittaker modules for the Virasoro algebra and obtain analogues to several results from the classical setting, including a classification of simple Whittaker modules by central characters and composition series for general Whittaker modules.
Whittaker Modules for W type Cartan Lie superalgebras
研究向量场李超代数$W_{m,n}$的Whittaker模范畴，通过建立与子代数$T_{m,n}$的有限维模范畴的等价，并利用覆盖技巧描述具有有限维Whittaker向量空间和非奇异参数$\mathbf{a}$的简单模。
Projective and Whittaker functors on category $\mathcal{O}$
本文证明了半单复李代数 BGG 范畴 $\mathcal{O}$ 正则块上的 Whittaker 函子可由平移至墙函子与 Soergel-Miličić 等价复合得到，并证明它是与所有投射函子及其自同态交换的商函子。
The category of Whittaker modules over the Cartan Type Lie algebra $\bar{S}_2$
研究$\mathbb{C}^2$上常散度多项式向量场李代数$\bar{S}_2$的Whittaker模，通过等价于抛物子代数有限维模范畴分类了所有单Whittaker模，并建立了与结合代数$H_{\mathbf{1}}$有限维模范畴的等价。
We construct categories of Harish-Chandra bimodules for affine Lie algebras analogous to Harish-Chandra bimodules with infinitesimal characters for simple Lie algebras, addressing an old problem raised by I. Frenkel and Malikov. Under an integrality hypothesis, we establish monoidal equivalences between blocks of our affine Harish-Chandra bimodules and versions of the affine Hecke category. To do so, we introduce a new singular localization onto Whittaker flag manifolds. The argument for the latter specializes to a somewhat alternative treatment of regular localization, and identifies the cate…
Whittaker categories, properly stratified categories and Fock space categorification for Lie superalgebras
本文研究I型Lie超代数的Whittaker模范畴，证明其等价于BGG范畴及Harish-Chandra双模奇异范畴的Serre商，并进一步证明这些范畴与Backelin函子一起范畴化了A型量子群的q-对称化Fock空间，其中典范基与倾斜对象、对偶典范基与单对象分别对应。
We construct weak (i.e. non-graded) modules over the vertex operator algebra $M(1)^+$, which is the fixed-point subalgebra of the higher rank free bosonic (Heisenberg) vertex operator algebra with respect to the $-1$ automorphism. These weak modules are constructed from Whittaker modules for the higher rank Heisenberg algebra. We prove that the modules are simple as weak modules over $M(1)^+$ and calculate their Whittaker type when regarded as modules for the Virasoro Lie algebra. Lastly, we show that any Whittaker module for the Virasoro Lie algebra occurs in this way. These results are a hig…
Whittaker categories of quasi-reductive Lie superalgebras and principal finite W-superalgebras
本文研究拟约化李超代数的Whittaker范畴，证明Backelin函子的不可约性，构造主有限W-超代数并建立Skryabin型等价，给出Soergel结构定理的超类比。
Whittaker modules and representations of finite $W$-algebras of queer Lie superalgebras
本文研究了 queer Lie超代数的 Whittaker 模块及其与有限 $W$-超代数的表示关系，提出了 Whittaker 模块的分类方法，并建立了与 BGG 类别的等价关系。
Super duality for Whittaker modules and finite $W$-algebras
本文通过建立Whittaker模块与有限$W$-代数之间的超双曲性，揭示了无限秩极限下模块范畴的等价关系。
For any positive integer $n$, let $A_n=\mathbb{C}[t_1,\dots,t_n]$, $W_n=\text{Der}(A_n)$ and $Δ_n=\text{Span}\{\frac{\partial}{\partial{t_1}},\dots,\frac{\partial}{\partial{t_n}}\}$. Then $(W_n, Δ_n)$ is a Whittaker pair. A $W_n$-module $M$ on which $Δ_n$ operates locally finite is called a Whittaker module. We show that each block $Ω_{\mathbf{a}}^{\widetilde{W}}$ of the category of $(A_n,W_n)$-Whittaker modules with finite dimensional Whittaker vector spaces is equivalent to the category of finite dimensional modules over $L_n$, where $L_n$ is the Lie subalgebra of $W_n$ consisting of vector …
On some non-principal locally analytic representations induced by Whittaker modules
本文研究由连通分裂约化p进李群的Whittaker模诱导的非主局部解析表示，证明其不可容许且拓扑不可约、朴素Jacquet函子对所有抛物子群消失，且不满足Kohlhaase的超尖点定义。
Whittaker Category and Finite W-superalgebras for Cartan Type Lie Superalgebras
研究Cartan型李超代数W(n)的Whittaker范畴，通过极小抛物子代数引入与幂零元e相关的Whittaker范畴并分类单对象，进而建立有限W-超代数表示范畴与弱Whittaker模范畴间的广义Skryabin等价。
We prove that the categories of Gelfand-Zeitlin modules of $\mathfrak{g}=\mathfrak{gl}_n$ and Whittaker modules associated with a semi-simple complex finite-dimensional algebra $\mathfrak{g}$ are extension full in the category of all $\mathfrak{g}$-modules. This is used to estimate and in some cases determine the global dimension of blocks of the categories of Gelfand-Zeitlin and Whittaker modules.
For a real reductive linear Lie group G, the space of Whittaker functions is the representation space induced from a non-degenerate unitary character of the Iwasawa nilpotent subgroup. Defined are the standard Whittaker (g,K)-modules, which are K-admissible submodules of the space of Whittaker functions. We first determine the structures of them when the infinitesimal characters characterizing them are generic. As an example of the integral case, we determine the composition series of the standard Whittaker (g,K)-module when G is the group U(n,1) and the infinitesimal character is regular inte…
Whittaker vectors in singular Whittaker modules
本文研究奇异 Whittaker 模，证明其单模性与 Whittaker 向量空间维数为 1 等价，并给出任意局部有限模中 Whittaker 向量维数的上界。
Whittaker modules for $U_q(\mathfrak{sl}_3)$
本文研究$U_q(\frak{sl}_3)$的惠特克模，构造泛惠特克模并分析其惠特克向量、子模、商模的不可约性及极大子模，发现其惠特克模型与$U_q(\frak{sl}_2)$等不同。
Quasi-Whittaker modules
本文提出拟Whittaker模的一般框架，引入Whittaker零化子判定其不可约性，并分类了多类李代数的不可约拟Whittaker模，获得高度2的不可约光滑$\mathcal{W}_n^+$-模。
We study a category of Whittaker modules over a complex semisimple Lie algebra by realizing it as a category of twisted D-modules on the associated flag variety using Beilinson-Bernstein localization. The main result of this paper is the development of a geometric algorithm for computing the composition multiplicities of standard Whittaker modules. This algorithm establishes that these multiplicities are determined by a collection of polynomials we refer to as Whittaker Kazhdan-Lusztig polynomials. In the case of trivial nilpotent character, this algorithm specializes to the usual algorithm fo…
We prove the irreducibility of the universal non-degenerate Whittaker modules for the affine Lie algebra $\widehat{sl_2}$ of type $A_1^{(1)}$ with noncritical level which are also irreducible Whittaker modules over $\widetilde{sl_2} =\widehat{sl_2} + {\Bbb C} d $ with the same Whittaker function and central charge. We have to modulo a central character for ${sl_2}$ to obtain irreducible degenerate Whittaker $\widehat{sl_2} $-modules with noncritical level. In the case of critical level the universal Whittaker module is reducible. We prove that the quotient of universal Whittaker $\widehat{sl_2…
Let $\mathcal{G}$ be the planar Galilean conformal algebra and $\widetilde{\mathcal{G}}$ be its universal central extension. Then $\mathcal{G}$ (resp. $\widetilde{\mathcal{G}}$) admits a triangular decomposition: $\mathcal{G}=\mathcal{G}^{+}\oplus\mathcal{G}^{0}\oplus\mathcal{G}^{-}$ (resp. $\widetilde{\mathcal{G}}=\widetilde{\mathcal{G}}^{+}\oplus\widetilde{\mathcal{G}}^{0}\oplus\widetilde{\mathcal{G}}^{-}$). In this paper, we study universal and generic Whittaker $\mathcal{G}$-modules (resp. $\widetilde{\mathcal{G}}$-modules) of type $ϕ$, where $ϕ:\mathcal{G}^{+}=\widetilde{\mathcal{G}}^{+}\…
We investigate Whittaker modules for generalized Weyl algebras, a class of associative algebras which includes the quantum plane, Weyl algebras, the universal enveloping algebra of sl_2 and of Heisenberg Lie algebras, Smith's generalizations of U(sl_2), various quantum analogues of these algebras, and many others. We show that the Whittaker modules V = Aw of the generalized Weyl algebra A = R(phi,t) are in bijection with the phi-stable left ideals of R. We determine the annihilator Ann_A(w) of the cyclic generator w of V. We also describe the annihilator ideal Ann_A(V) under certain assumption…
For any $n\in \mathbb{Z}_{\geq 2}$, let $\mathfrak{m}_n$ be the subalgebra of $\mathfrak{sp}_{2n}$ spanned by all long negative root vectors $X_{-2ε_i}$, $i=1,\dots,n$. An $\mathfrak{sp}_{2n}$-module $M$ is called a Whittaker module with respect to the Whittaker pair $(\mathfrak{sp}_{2n},\mathfrak{m}_n)$ if the action of $\mathfrak{m}_n$ on $M$ is locally finite, according to a definition of Batra and Mazorchuk. This kind of modules are more general than the classical Whittaker modules defined by Kostant. In this paper, we show that each non-singular block $\mathcal{WH}_{\mathbf{a}}^μ$ with fi…
In this paper we construct a family of exact functors from the category of Whittaker modules of the simple complex Lie algebra of type $A_n$ to the category of finite-dimensional modules of the graded affine Hecke algebra of type $A_\ell$. Using results of Backelin and of Arakawa-Suzuki, we prove that these functors map standard modules to standard modules (or zero) and simple modules to simple modules (or zero). Moreover, we show that each simple module of the graded affine Hecke algebra appears as the image of a simple Whittaker module. Since the Whittaker category contains the BGG category …
Let $\mathfrak{g}$ be a complex semisimple Lie algebra. We give a classification of contravariant forms on the nondegenerate Whittaker $\mathfrak{g}$-modules $Y(χ, η)$ introduced by Kostant. We prove that the set of all contravariant forms on $Y(χ, η)$ forms a vector space whose dimension is given by the cardinality of the Weyl group of $\mathfrak{g}$. We also describe a procedure for parabolically inducing contravariant forms. As a corollary, we deduce the existence of the Shapovalov form on a Verma module, and provide a formula for the dimension of the space of contravariant forms on the deg…
Whittaker constructions for quantum affine algebras
本文通过抛物诱导从Heisenberg李代数的不可约Whittaker模构造了无扭仿射Kac-Moody李代数的虚Whittaker模，建立了不可约性判据，并推广到量子仿射代数情形，同时证明了$\mathcal{U}_q(A_1^{(1)})$上一类非量子形变模的不可约性。
Two proofs of a Jantzen Conjecture for Whittaker Modules
本文定义了复半单李代数上标准 Whittaker 模的滤过并证明其基本性质，将 Jantzen 猜想推广至 Whittaker 模，并分别通过代数和几何方法给出了两个证明。
In this paper we construct weighted path models to compute Whittaker vectors in the completion of Verma modules, as well as Whittaker functions of fundamental type, for all finite-dimensional simple Lie algebras, affine Lie algebras, and the quantum algebra $U_q(\mathfrak{sl}_{r+1})$. This leads to series expressions for the Whittaker functions. We show how this construction leads directly to the quantum Toda equations satisfied by these functions, and to the $q$-difference equations in the quantum case. We investigate the critical limit of affine Whittaker functions computed in this way.
In this paper, the property and the classification the simple Whittaker modules for the schrödinger algebra are studied. A quasi-central element plays an important role in the study of Whittaker modules of level zero. For the Whittaker modules of nonzero level, our arguments use the Casimir element of semisimple Lie algebra $sl_2$ and the description of simple modules over conformal Galilei algebras by R. Lü, V. Mazorchuk and K. Zhao.
Motivated by the study of invariant rings of finite groups on the first Weyl algebras $A_{1}$ (\cite{AHV}) and finding interesting families of new noetherian rings, a class of algebras similar to $U(sl_{2})$ were introduced and studied by Smith in \cite{S}. Since the introduction of these algebras, research efforts have been focused on understanding their weight modules, and many important results were already obtained in \cite{S} and \cite{Ku}. But it seems that not much has been done on the part of nonweight modules. In this note, we generalize Kostant's results in \cite{K} on the Whittaker …
We classify contravariant pairings between standard Whittaker modules and Verma modules over a complex semisimple Lie algebra. These contravariant pairings are useful in extending several classical techniques for category $\mathcal{O}$ to the Miličić--Soergel category $\mathcal{N}$. We introduce a class of costandard modules which generalize dual Verma modules, and describe canonical maps from standard to costandard modules in terms of contravariant pairings. We show that costandard modules have unique irreducible submodules and share the same composition factors as the corresponding standard …
In 1978 Kostant suggested the Whittaker model of the center of the universal enveloping algebra U(g) of a complex simple Lie algebra g. The main result is that the center of U(g) is isomorphic to a commutative subalgebra in U(b), where b is a Borel subalgebra in g. This observation is used in the theory of principal series representations of the corresponding Lie group G and in the proof of complete integrability of the quantum Toda lattice. In this paper we generalize the Kostant's construction to quantum groups. In our construction we use quantum analogues of regular nilpotent elements defin…
On the Self-adjoint properties of the standard Whittaker $(\mathfrak{g}, K)$-modules
研究实分裂约化线性李群下标准惠特克$(\mathfrak{g}, K)$-模，确定其整体特征，证明有自伴结构，还得出秩为二的分裂群如$SL(3,\mathbb{R})$等的该模的明确基座滤过。
We identify q-deformed gl(l+1)-Whittaker functions with a specialization of Macdonald polynomials. This provides a representation of q-deformed gl(l+1)-Whittaker functions in terms of Demazure characters of affine Lie algebra \hat{gl(l+1)}. We also define a system of dual Hamiltonians for q-deformed gl(l+1)-Toda chains and give a new integral representation for q-deformed gl(l+1)-Whittaker functions. Finally an expression of q-deformed gl(l+1)-Whittaker function as a matrix element of a quantum torus algebra is derived.
Kazhdan-Lusztig Algorithm for Whittaker Modules with Arbitrary Infinitesimal Characters
本文针对复半单李代数，给出了具有任意无穷小特征的不可约 Whittaker 模的特征描述及 Kazhdan-Lusztig 算法，推广了已有结果并恢复了 Verma 模的非整猜想。
We prove that the radial part of the class one Whittaker function on a split semisimple Lie group can be obtained as an appropriate limit of the Heckman-Opdam hypergeometric function.
Generalized Laguerre functions and Whittaker vectors for holomorphic discrete series
本文在四种实现下刻画管型 Hermitian Lie 群全纯离散级数中的退化 Whittaker 向量，给出其显式 $K$-型展开，并通过对称锥上的广义 Laguerre 函数联系生成函数与递推关系。
In this article we study the perverse sheaf on Drinfeld's compactification obtained by applying the geometric Jacquet functor (alias nearby cycles) to a nondegenerate Whittaker sheaf. Namely, we describe its restrictions along the defect stratification in terms of the Langlands dual Lie algebra, in particular showing that this nearby cycles sheaf is tilting. We also describe the subquotients of the monodromy filtration using the Picard-Lefschetz oscillators introduced by S. Schieder, including a proof that the subquotients are semisimple without reference to any theory of weights. This argumen…
Equivariant Satake category and Kostant-Whittaker reduction
本文通过equivariant导出范畴和Harish-Chandra双模，推导出affine Grassmannian的loop-rotation equivariant同调与量子化Toda lattice的联系。
Let $W_{m|n}$ be the (finite) $W$-algebra attached to the principal nilpotent orbit in the general linear Lie superalgebra $\mathfrak{gl}_{m|n}(\mathbb{C})$. In this paper we study the {\em Whittaker coinvariants functor}, which is an exact functor from category $\mathcal O$ for $\mathfrak{gl}_{m|n}(\mathbb{C})$ to a certain category of finite-dimensional modules over $W_{m|n}$. We show that this functor has properties similar to Soergel's functor $\mathbb V$ in the setting of category $\mathcal O$ for a semisimple Lie algebra. We also use it to compute the center of $W_{m|n}$ explicitly, and …
Generally speaking, this thesis focuses on the interplay between the representations of Lie groups and probability theory. It subdivides into essentially three parts. In a first rather algebraic part, we construct a path model for geometric crystals in the sense of Berenstein and Kazhdan, for complex semi-simple Lie groups. We will mainly describe the algebraic structure, its natural morphisms and parameterizations. The theory of total positivity will play a particularly important role. Then, we anticipate on the probabilistic part by exhibiting a canonical measure on geometric crystals. It us…
The Heisenberg-Virasoro Lie conformal superalgebra
本文引入 Heisenberg-Virasoro 李共形超代数并定义 Ramond 型超 Heisenberg-Virasoro 代数，构造了一类包含最高权模、Whittaker 模及高阶 Whittaker 模的单模，并给出同构于 Neveu-Schwarz 型的子代数。
For a semi-simple simply connected algebraic group G we introduce certain parabolic analogues of the Nekrasov partition function (introduced by Nekrasov and studied recently by Nekrasov-Okounkov and Nakajima-Yoshioka for G=SL(n)). These functions count (roughly speaking) principal G-bundles on the projective plane with a trivialization at infinity and with a parabolic structure at the horizontal line. When the above parabolic subgroup is a Borel subgroup we show that the corresponding partition function is basically equal to the Whittaker matrix coefficient in the universal Verma module over c…
We give a proof of the recursive formula on the norm of Whittaker vector of the deformed Virasoro algebra, which is an analog of the one for the Virasoro Lie algebra proposed by Al. Zamolodchikov. Our formula gives a proof of the pure SU(2) 5d AGT relation proposed by Awata and Yamada. We also give a summary of the structures of the deformed Virasoro algebra and the fundamental properties of the Verma module.
Affine W-algebras are a somewhat complicated family of (topological) associative algebras associated with a semisimple Lie algebra, quantizing functions on the algebraic loop space of Kostant's slice. They have attracted a great deal of attention in geometric representation theory because of Feigin-Frenkel's duality theorem for them, which identifies W-algebras for a Lie algebra and its Langlands dual through a subtle construction. The main result of this paper is an affine version of Skryabin's theorem, describing the category of modules over the W-algebra in simpler categorical terms. But un…
Whittaker modules of central extensions of Takiff superalgebras and finite supersymmetric $W$-algebras
本文研究Takiff超代数中心扩张的Whittaker模范畴，证明其与对应基本经典李超代数的Whittaker模范畴等价，进而得到超对称有限W-代数与主有限W-超代数的模等价，实现了主有限超对称W-代数不可约表示的分类与构造。
The holomorphic discrete series contribution to the generalized Whittaker Plancherel formula
本文研究了管型Hermitian李群中全纯离散级数对广义Whittaker Plancherel公式的贡献，构造了广义Whittaker向量嵌入并给出了其形式维数的显式公式及Hardy型空间解释。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。