Classification of irreducible modules for the vertex operator algebra M(1)^+
Chongying Dong, Kiyokazu Nagatomo
在-1自同构下，对秩为1的自由玻色VOA的不动点顶点算子子带的不可约模进行了分类。
We classify the irreducible modules for the fixed point vertex operator subebra of the rank 1 free bosonic VOA under the -1 automorphism.
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Classification of irreducible modules for the vertex operator algebra M(1)^+, II: higher rank
顶点算子代数M（1）^+是自由玻色顶点算子代数M（1）在-1自同构下的不动点集。本文对M（1）^+的所有不可约模进行了分类.
Classification of irreducible modules for the vertex operator algebra V_L^+: General case
对任意正定偶格L上的顶点算子代数V_L的不动点顶点算子子代数V_L^+在L的-1等距提升的自同构下的不可约模进行了分类.
Classification of irreducible modules of the vertex algebra $V_L^+$ when $L$ is a nondegenerate even lattice of an arbitrary rank
当$L$是任意秩的负定偶格时，本文首先对顶点代数$V_L^+$的所有不可约模进行了分类.特别地，我们证明了任何不可约$V_L^+$ -模同构于不可约扭$V_L$ -模的子模。当$L$是有限秩的非退化偶格时，我们将这个结果推广到顶点代数$V_L^+$.
Classification of irreducible modules of certain subalgebras of free boson vertex algebra
设M（1）是单个自由玻色子的顶点代数。对M（1）的某些顶点子代数的由两个生成元生成的不可约模进行了分类。这些子代数对应于具有中心电荷$1- 6 \frac{(p - 1) ^{2}}{p}$的W（2，2 p-1）-代数，其中p是正整数，$p \ge 2$ .我们还确定了相关的朱代数。
Let $V_{L}$ be the vertex algebra associated to a non-degenerate even lattice $L$, $θ$ the automorphism of $V_{L}$ induced from the $-1$ symmetry of $L$, and $V_{L}^{+}$ the fixed point subalgebra of $V_{L}$ under the action of $θ$. We classify the irreducible weak $V_{L}^{+}$-modules and show that any irreducible weak $V_{L}^{+}$-module is isomorphic to a weak submodule of some irreducible weak $V_{L}$-module or to a submodule of some irreducible $θ$-twisted $V_{L}$-module.
In this paper, for every $ε\in \mathbb{Z}$, we introduce an extension of the 2-toroidal Lie algebra by certain derivations. Based on the $ϕ_ε$-coordinated modules theory for vertex algebras, we give an explicit realization of a class of irreducible highest weight modules for this extended toroidal Lie algebra. When $ε=1$, this affords a realization of certain irreducible modules for the toroidal extended affine Lie algebras first constructed by Billig.
Let $V_{L}$ be the vertex algebra associated to a non-degenerate even lattice $L$, $θ$ the automorphism of $V_{L}$ induced from the $-1$ symmetry of $L$, and $V_{L}^{+}$ the fixed point subalgebra of $V_{L}$ under the action of $θ$. In this series of papers, we classify the irreducible weak $V_{L}^{+}$-modules and show that any irreducible weak $V_{L}^{+}$-module is isomorphic to a weak submodule of some irreducible weak $V_{L}$-module or to a submodule of some irreducible $θ$-twisted $V_{L}$-module. Let $M(1)^{+}$ be the fixed point subalgebra of the Heisenberg vertex operator algebra $M(1)$ …
Let $V_{L}$ be the vertex algebra associated to a non-degenerate even lattice $L$, $θ$ the automorphism of $V_{L}$ induced from the $-1$-isometry of $L$, and $V_{L}^{+}$ the fixed point subalgebra of $V_{L}$ under the action of $θ$. In this series of papers, we classify the irreducible weak $V_{L}^{+}$-modules and show that any irreducible weak $V_{L}^{+}$-module is isomorphic to a weak submodule of some irreducible weak $V_{L}$-module or to a submodule of some irreducible $θ$-twisted $V_{L}$-module. In this paper (Part 1), we show that when the rank of $L$ is $1$, every non-zero weak $V_{L}^{…
The irreducible modules of the 2-cycle permutation orbifold models of lattice vertex operator algebras of rank 1 are classified, the quantum dimensions of irreducible modules and the fusion rules are determined.
The irreducible modules for the parafermion vertex operator algebra associated to any finite dimensional Lie algebra and any positive integer are identified, the quantum dimensions are computed and the fusion rules are determined.
Representations of Centrally-Extended Lie Algebras over Differential Operators and Vertex Algebras
通过具有有限个非零元素的无限矩阵的中心扩张经典李代数的某些不可约模，构造了圆上微分算子的左理想上的中心扩张经典李代数的不可约模.确定了与这些代数的真空表示相关的顶点代数的结构。证明了在一定条件下，有限个非零元素的无穷矩阵的中心扩张经典李代数的最高权不可约模一般地产生这些顶点代数的单子元的不可约模.我们的结果是与仿射Kac-Moody代数相关的共形域论中著名的WZW模型的自然推广。它们也可以被看作是自由域论的二次推广。
In this paper, under the assumption that the diagonal coset vertex operator algebra $C(L_{\mathfrak g}(k+l,0),L_{\mathfrak g}(k,0)\otimes L_{\mathfrak g}(l,0))$ is rational and $C_2$-cofinite, the global dimension of $C(L_{\mathfrak g}(k+l,0),L_{\mathfrak g}(k,0)\otimes L_{\mathfrak g}(l,0))$ is obtained, the quantum dimensions of multiplicity spaces viewed as $C(L_{\mathfrak g}(k+l,0),L_{\mathfrak g}(k,0)\otimes L_{\mathfrak g}(l,0))$-modules are also obtained. As an application, a method to classify irreducible modules of $C(L_{\mathfrak g}(k+l,0),L_{\mathfrak g}(k,0)\otimes L_{\mathfrak g}(…
Finite-dimensional irreducible $U_q(\mathfrak{sl}_2)$-modules from the equitable point of view
本文研究了量子代数$U_q(\mathfrak{sl}_2)$，其中$q$不是单位根.本文从公平表示的观点出发，给出了有限维不可约$U_q(\mathfrak{sl}_2)$ -模的刻画。
Tensor products of strongly graded vertex algebras and their modules
研究了强分次顶点代数及其强分次分次模，它们是共形顶点代数及其模，它们具有由满足一定分次限制条件的阿贝尔群进行的第二相容分次.考虑强分次顶点代数的张量积及其张量积强分次模。证明了强分次顶点代数的张量积的强分次不可约模的张量积是不可约的，并且证明了在等价的条件下，强分次顶点代数的张量积的强分次不可约模是自然定义的.证明了张量积强分次顶点代数的某些自然定义的强分次模是完全可约的当且仅当每个张量积因子的强分次模都是完全可约的.这些结果推广了顶点算子代数及其模的相应已知结果。
On intertwining operators and finite automorphism groups of vertex operator algebras
设V是单顶点算子代数，G是有限自同构群.利用V的交织算子，给出了作为不可约V-模的子模出现的不可约V^G-模的交织算子的构造.作为应用，我们还确定了顶点算子代数的融合规则.
In this paper, we study Virasoro vertex algebras and affine vertex algebras over a general field of characteristic $p>2$. More specifically, we study certain quotients of the universal Virasoro and affine vertex algebras by ideals related to the $p$-centers of the Virasoro algebra and affine Lie algebras. Among the main results, we classify their irreducible $\mathbb{N}$-graded modules by explicitly determining their Zhu algebras and show that these vertex algebras have only finitely many irreducible $\mathbb{N}$-graded modules and they are $C_2$-cofinite.
Classifications of Simple Novikov Algebras and Their Irreducible Modules of Characteristic 0
本文首先给出了特征为0的代数闭域上无限维单Novikov代数的一个分类定理。然后，我们对具有左作用局部有限的幂等元的无限维单Novikov代数的所有不可约模进行了分类。
Vertex operator algebras, generalized doubles and dual pairs
设V是单顶点算子代数，G是有限自同构群.则在所有不等价的不可约V-模的集合上存在自然右G-作用。设S是在G作用下闭的不可约V-模的有限集。存在有限维半单结合代数A_α（G，S），其中A_α（G，S）与顶点算子代数V^G在Howe意义下构成S中V-模之和的对偶对，且A_α（G，S）是由S上的G-作用自然确定的2-上圈α.特别地，每个不可约V-模都是完全可约V^G-模。
Let $V$ be a simple vertex algebra of countable dimension, $G$ be a finite automorphism group of $V$ and $σ$ be a central element of $G$. Assume that ${\cal S}$ is a finite set of inequivalent irreducible $σ$-twisted $V$-modules such that ${\cal S}$ is invariant under the action of $G$. Then there is a finite dimensional semisimple associative algebra ${\cal A}_α(G,{\cal S})$ for a suitable $2$-cocycle $α$ naturally determined by the $G$-action on ${\cal S}$ such that $({\cal A}_α(G,{\cal S}),V^G)$ form a dual pair on the sum $\cal M$ of $σ$-twisted $V$-modules in ${\cal S}$ in the sense that …
Irreducible highest-weight modules and equivariant quantization
我们推广[KMST]的结果有关的等变量化的韦尔马模$M(λ)$的通用重量$λ$的情况下，一般的$λ$。我们考虑了半单复李代数的不可约最高权模上的Shapovalov形式、融合元和等变量子化之间的关系。我们还讨论了熔合元素的一些极限性质。[KMST] E. Karolinsky和A. Stolin，动力学杨-巴克斯特方程，准泊松齐性空间和量子化，Lett.数学物理，71（2005），第179 -197页; e-print math.QA/0309203。
Irreducible Virasoro modules from irreducible Weyl modules
利用Block的结果对微分算子代数$\mathbb{C}[t,t^{-1}, \frac d{dt}]$上的不可约模进行了分类.从这个分类出发，利用“扭曲技巧”，我们构造了Virasoro代数上许多新的不可约模。这些新的不可约Virasoro模一般不是权模。我们确定了两个这样的不可约Virasoro模同构的充要条件。文末给出了具有不同特征的不可约Virasoro模的例子。特别地，不可约Virasoro模块类$Ω(λ, b)$定义在多项式代数$\mathbb{C}[x]$上。
Z_3 symmetry and W_3 algebra in lattice vertex operator algebras
利用陪集构造和轨道折叠理论，将中心荷为6/5的W3代数实现为与\sqrt{2} A2型格相关联的顶点算子代数V_{ \sqrt{2} A2}的子代数.证明了W_3是有理数。它的不可约模的分类和明确的建设。并计算了这些不可约模的特征标。
We study $\N$-graded $ϕ$-coordinated modules for a general quantum vertex algebra $V$ of a certain type in terms of an associative algebra $\widetilde{A}(V)$ introduced by Y.-Z. Huang. Among the main results, we establish a bijection between the set of equivalence classes of irreducible $\N$-graded $ϕ$-coordinated $V$-modules and the set of isomorphism classes of irreducible $\widetilde{A}(V)$-modules. We also show that for a vertex operator algebra, rationality, regularity, and fusion rules are independent of the choice of the conformal vector.
$C_2$-cofiniteness of the vertex algebra $V_L^+$ when $L$ is a non-degenerate even lattice
Abe，Buhl和Dong证明了当$L$是正定偶格时，顶点代数$V_L^+$及其不可约弱模满足$C_2$-有限性条件.本文推广了他们的结果，证明了当$L$是负定偶格和当$L$是既不负定也不正定的非退化偶格时，顶点代数$V_L^+$及其不可约弱模是$C_2$ -余有限的.
Level two irreducible representations of $U_q(\widehat{sl}_2)$, vertex operators, and their correlations
与第二层$U_q(\widehat{sl}_2)$模块相关的顶点算子使用玻色子和费米子显式构造。导出了顶点算子乘积迹的积分公式。应用这些结果给出了可积$S=1$量子自旋链的$n$点自旋关联函数，推广了Jimbo { \em et al}对$S=1/2$情形的工作.
Classification of irreducible weight modules with a finite dimensional weight space over twisted Heisenberg-Virasoro algebra
证明了扭Heisenberg-Virasoro代数上具有无限维权空间的不可约权模的支撑与权格重合，且这种模的所有非平凡权空间都是无限维的.作为推论，我们得到了扭Heisenberg-Virasoro代数上的每个具有非平凡有限维权空间的不可约权模都是Harish-Chandra模（因此是不可约的最高或最低权模，或者是来自中间级数的不可约模
Irreducible Modules for the Quantum Affine Algebra $U_q(g)$ and its Borel subalgebra $U_q(g)^{\geq 0}$
证明了任意量子仿射代数$U_q(g)$的有限维不可约模与其Borel子代数$U_q(g)^{\geq 0}$的有限维不可约模之间的双射。
On the classification of finite dimensional irreducible modules for affine BMW algebras
本文对具有任意特征的代数闭域上的仿射BMW代数的有限维不可约模进行了分类。
Classification of irreducible weight modules over $W$-algebra W(2,2)
证明了$W$ -代数$W(2, 2)$上具有无穷维权空间的不可约权模的支集与权格重合，并且证明了这种模的所有非平凡权空间都是无穷维的.作为推论，我们得到了$W$ -代数$W(2, 2)$上的每一个具有非平凡有限维权空间的不可约权模都是Harish-Chandra模（因此是不可约的最高或最低权模或中间级数的不可约模）.
The N = 1 Triplet Vertex Operator Superalgebras: Twisted Sector
我们对最近引入的N=1超三元顶点算子超代数$σ$ [Adamovic D.，Milas A.，通信数学物理，出现，arXiv：0712.0379]。还确定了$σ$ -扭模的不可约分次维数。这些结果与我们以前在非扭曲情形下的工作相结合，证明了由不可约特征标、不可约超特征标和$σ$ -扭曲不可约特征标所张成的空间的$SL(2,\mathbb{Z})$ -闭包是$(9m+3)$ -维的.我们提出了强有力的证据，这也是（全）空间的广义字符$\mathcal{SW}(m)$。我们还能够将不可约$\mathcal{W}(2m+1)$字符与在[Adamovic D.，Milas A.，217（2008），2664-2699，arXiv：0707.1857]。
In this paper we classified irreducible modules for the loop of derivations of rational quantum torus with associative $\mathbb{C}_q^1\otimes B$ action and anti-associative $\mathbb{C}_q^2\otimes B$ action on the modules.
A Class of Irreducible Modules for the Extended Affine Lie Algebra $\widetilde{\frak{gl}_l({\mathbb{C}_q})}$
利用自由域构造了广义仿射李代数$\widetilde{\frak{gl}_l({\bc_q})}$的一类模.给出了这类模不可约的一个充要条件。
An algorithm to compute the canonical basis of an irreducible Uq(g)-module
本文给出了有限维半单李代数的量子化包络代数上不可约模的标准基的计算方法。该算法适用于构造为具有已知规范基的模块的张量积的子模块的模块。
In this paper, the irreducible modules for the $\mathbb{Z}_{2}$-orbifold vertex operator subalgebra of the parafermion vertex operator algebra associated to the irreducible highest weight modules for the affine Kac-Moody algebra $A_1^{(1)}$ of level $k$ are classified and constructed.
An algorithm for computing the global basis of an irreducible $U_{q}(sp_{2n})$-module
我们描述了一个简单的算法计算任何有限维$U_{q}(sp_{2n})$ -模的典范基。
A New Proof for Classification of Irreducible Modules of a Hecke Algebra of Type $ A_n$
本文给出了G. E. 1995年，墨菲。
An algorithm for computing the global basis of a finite dimensional irreducible $U_{q}(so_{2n+1})$ or $U_{q}(so_{2n})$-module
我们描述了一个简单的算法计算任何不可约有限维$U_{q}(so_{2n+1})$或$U_{q}(so_{2n})$ -模的典范基。
For an irreducible module $P$ over the Weyl algebra $\mathcal{K}_n^+$ (resp. $\mathcal{K}_n$) and an irreducible module $M$ over the general liner Lie algebra $\mathfrak{gl}_n$, using Shen's monomorphism, we make $P\otimes M$ into a module over the Witt algebra $W_n^+$ (resp. over $W_n$). We obtain the necessary and sufficient conditions for $P\otimes M$ to be an irreducible module over $W_n^+$ (resp. $W_n$), and determine all submodules of $P\otimes M$ when it is reducible. Thus we have constructed a large family of irreducible weight modules with many different weight supports and many irred…
Extension of vertex operator algebra $V_{\hat{H}_{4}}(\ell,0)$
在一定的自然条件下，对仿射Nappi-Witten李代数$\hat{H}_{4}$的不可约限制模进行了分类.事实证明，$\hat{H}_{4}$的表示论与海森堡代数的表示理论有很大的不同。我们还研究了顶点算子代数$V_{\hat{H}_{4}}(\ell,0)$的偶格$L$扩张.通过将$V_{\hat{H}_{4}}(\ell,0)$看作顶点代数的不可约表示，给出了扩张$V_{\hat{H}_{4}}(\ell,0)\otimes \C[L]$及其不可约模的结构.
Characters of irreducible modules with non-critical highest weights over affine Lie algebras
利用平移函子、Enright函子和Jantzen的变形论证，从有理情形出发，导出仿射李代数上具有任意非临界最高权的不可约模的Kazhdan-Lusztig型特征标公式.
Lie conformal algebras $\mathcal{W}(a,b)$ are the semi-direct sums of Virasoro Lie conformal algebra and its nontrivial conformal modules of rank one. In this paper, we first give a complete classification of all finite nontrivial irreducible conformal modules of $\mathcal{W}(a,b)$. It is shown that all such modules are of rank one. Moreover, with a similar method, all finite nontrivial irreducible conformal modules of Schrödinger-Virasoro type Lie conformal algebras $TSV(a,b)$ and $TSV(c)$ are characterized.
Jones Wenzl projectors in tensor products of a Verma module and irreducible modules
该研究在 $U_q(\mathfrak{sl}_2)$ 框架下，于 Verma 模与多个二维不可约模的张量积自同态空间中构造类似 Jones Wenzl 投影算子的特殊幂等元。
A classification of irreducible Wakimoto modules for the affine Lie algebra $A_1 ^{(1)}$
通过使用arXiv：math/0602181中开发的方法，我们研究了$\widehat{sl_2}$的某些Wakimoto模在临界水平上的不可约性。我们对所有的$χ\in {\Bbb C}((z))$进行分类，使得相应的Wakimoto模$W_χ$是不可约的。结果表明，Schur多项式的零点在分类结果中起着重要的作用。
In this paper, we continue the study on toroidal vertex algebras initiated in \cite{LTW}, to study concrete toroidal vertex algebras associated to toroidal Lie algebra $L_{r}(\hat{\frak{g}})=\hat{\frak{g}}\otimes L_r$, where $\hat{\frak{g}}$ is an untwisted affine Lie algebra and $L_r=$\mathbb{C}[t_{1}^{\pm 1},\ldots,t_{r}^{\pm 1}]$. We first construct an $(r+1)$-toroidal vertex algebra $V(T,0)$ and show that the category of restricted $L_{r}(\hat{\frak{g}})$-modules is canonically isomorphic to that of $V(T,0)$-modules.Let $c$ denote the standard central element of $\hat{\frak{g}}$ and set $S…
Representations of N=2 superconformal vertex algebra
设$L_c$是与中心荷为$c$的N=2超共形代数的真空表示相关联的单顶点算子超代数（SVOA）.让$c_m = {3m}/{m+2}$。我们对SVOA $L_{c_m}$的所有不可约模进行了分类。当$m$为整数时，证明了以$c_m$为中心的N=2超共形代数的所有酉表示的集合提供所有不可约的$L_{c_m}$ -模.当$m \notin {\N} $和$m$是一个容许有理数时，我们证明了不可约$L_{c_m}$ -模可参数化为一个有限集的并和多条有理曲线的并.
Regularity of rational vertex operator algebras
正则顶点算子代数是使得任何弱模（不分次）是普通不可约模的直和的顶点算子代数。本文给出了有理顶点算子代数正则的几个充分条件。证明了与水平$l,$的仿射代数的可积表示相关联的月光模顶点算子代数$V^{\natural},$、顶点算子代数$L(l,0)$、与维拉索罗代数的离散级数的不可约最高权表示相关联的顶点算子代数$L(c_{p,q},0)$以及与正定偶格$L$相关联的顶点算子代数$V_L$是正则的.我们对$L(l,0)$的结果意味着任何水平$l$的限制可积模对于相应的仿射李代数是不可约最高权可积模的直和。空间$V_L$一般是顶点代数，如果$L$不是正定的.在这种情况下，我们建立了任何弱模的完全约化。
The decomposition of level-1 irreducible highest weight modules with respect to the level-0 actions of the quantum affine algebra $U'_q(\hat{sl}_n)$
我们分解了量子仿射代数$U_q(\hat{sl}_n)$关于q-alg/9702024中定义的0级$U'_q (\hat{sl}_n)$-作用的1级不可约最高权模。分解是由边界条型的斜杨图参数化的。
Crystal graphs of irreducible $U_v(\hat{sl}_e)$-modules of level two and Uglov bipartitions
我们给出了一个简单的描述之间的自然双射集的FLOTW双分区和一组的Uglov双分区（推广的Kleshchev双分区）。这些二分划，标签的晶体图的不可约$\mathcal{U}\_v({\hat{\mathfrak{sl}}\_e})$ -模块的水平二，自然出现在背景下的模表示理论的赫克代数类型$B\_n$。
Let d \subset d' be finite-dimensional Lie algebras, H = U(d), H'=U(d') the corresponding universal enveloping algebras endowed with the cocommutative Hopf algebra structure. We show that if L is a primitive Lie pseudoalgebra over H then all finite irreducible L' = Cur_H^{H'} L-modules are of the form Cur_H^{H'} V, where V is an irreducible L-module, with a single class of exceptions. Indeed, when L = H(d, χ, ω), we introduce non current L'-modules that are obtained by modifying the current pseudoaction with an extra term depending on an element t \in \d' \setminus d, which must satisfy some t…
$C_2$ cofiniteness and rationality of $V_{L_2}^{S_4}$ are obtained, and irreducible $V_{L_2}^{S_4}$-modules are classified. With the assumption of rationality and $C_2$ cofiniteness, irreducible $V_{L_2}^{A_5}$-modules are determined. Also, quantum dimensions of these irreducible modules are calculated.
Classification of irreducible modules of W_3 algebra with c = -2
利用自由玻色子域构造了c = -2的W_3代数上的不可约模V_α，α \in \C.证明了这些模穷尽了c =-2的W_3代数的所有不可约模。模V_α、α \in \C相对于W_3代数的全（二维）Cartan子代数的最高权为（α（α-1）/2，α（α-1）（2α-1）/6）。它们由有理曲线w^2 - t^2（8 t + 1）/9 = 0上的点（t，w）参数化。对顶点代数W_{1+\infty}中c = -1的不可约模进行了分类.
Vertex operator algebras associated to admissible representations of $\hat{sl}_2$
从顶点算子代数的角度研究了$\hat{sl}_2$的容许模.如果$l$是有理数，使得对于某些互质正整数$p\ge 2$和$q$，$l+2={p\over q}$，Kac和Wakimoto发现了$\hat{sl}_2$的许多不同的不可约表示，称为容许表示.本文证明了当$l$不是正整数时，与$l$的不可约最高权表示相关联的顶点算子代数$L(l,0)$不是有理数.然而，如果我们以某种方式改变维拉索罗代数，$L(l,0)$成为一个有理顶点算子代数，其不可约表示正是那些容许表示。证明了新的维拉索罗代数的$q$ -维数是模函数.我们还计算了核聚变规则。
An irreducible module for the parafermion vertex operator algebra $K(\mathfrak{sl}_2,k)$ is said to be of $σ$-type if an automorphism of the fusion algebra of $K(\mathfrak{sl}_2,k)$ of order $k$ is trivial on it. For any integer $k \ge 3$, we show that there exists an automorphism of order $2$ of the subalgebra of the fusion algebra of $K(\mathfrak{sl}_2,k)^{\langle θ\rangle}$ spanned by the irreducible direct summands of $σ$-type irreducible $K(\mathfrak{sl}_2,k)$-modules, where $θ$ is an involution of $K(\mathfrak{sl}_2,k)$. We discuss some examples of such an automorphism as well.
The Quantized Knizhnik-Zamolodchikov Equation in Tensor Products of Irreducible sl(2)-Modules
本文考虑量子化的Knizhnik-Zamolodchikov差分方程（qKZ），其值为不可约sl（2）模的张量积，该方程是用有理R-矩阵定义的.我们解决的多维q-超几何积分方程。我们用量子群$U_qsl(2)$上相应模的张量积来确定qKZ方程的解的空间。我们用三角R-矩阵计算qKZ方程的单值性。
The Automorphism Group of the Vertex Operator Algebra $V_L^+$ for an even lattice $L$ without roots
利用顶点算子代数$V_L^+$在不可约$V_L^+$ -模的同构类上的作用，研究了顶点算子代数的自同构群.特别地，当$L$同构于没有根的偶幺模格时，$V_L^+$的自同构群的形状被确定，对于$ADE$类型的不可约根格$R$和秩为16的巴恩斯-沃尔格，$\sqrt2R$。
In this paper we classify all simple weight modules for a quantum group $U_q$ at a complex root of unity $q$ when the Lie algebra is not of type $G_2$. By a weight module we mean a finitely generated $U_q$-module which has finite dimensional weight spaces and is a sum of those. Our approach follows the procedures used by S. Fernando and O. Mathieu to solve the corresponding problem for semisimple complex Lie algebras.
Irreducible Modules for the Quantum Affine Algebra $U_q(\hat{sl}_2)$ and its Borel subalgebra $U_q(\hat{sl}_2)^{\geq 0}$
设$U_q(\hat{sl}_2)^{\geq 0}$表示量子仿射代数$U_q(\hat{sl}_2)$的Borel子代数.我们证明了对于集合${1,-1}$中的标量$ε_0, ε_1$的任何选择，以下成立。(i)设$V$是$(ε_0,ε_1)$类型的有限维不可约$U_q(\hat{sl}_2)^{\geq 0}$ -模。则$U_q(\hat{sl}_2)^{\geq 0}$对$V$的操作唯一地扩展为$U_q(\hat{sl}_2)$对$V$的操作。在$V$上得到的$U_q(\hat{sl}_2)$ -模块结构是不可约的，并且是$(ε_0,ε_1)$类型。(ii)设$V$是$(ε_0,ε_1)$类型的有限维不可约$U_q(\hat{sl}_2)$ -模。当$U_q(\hat{sl}_2)$ -操作限制为$U_q(\hat{sl}_2)^{\geq 0}$时，$V$上生成的$U_q(\hat{sl}_2)^{\geq 0}$ -模块结构是不可约的，类型为$(ε_0,ε_1)$。
In vertex algebra theory, fusion rules are described as the dimension of the vector space of intertwining operators between three irreducible modules. We describe fusion rules in the category of weight modules for the Weyl vertex algebra. This way we confirm the conjecture on fusion rules based on the Verlinde algebra. We explicitly construct intertwining operators appearing in the formula for fusion rules. We present a result which relates irreducible weight modules for the Weyl vertex algebra to the irreducible modules for the affine Lie superalgebra $\widehat{gl(1 \vert 1)}$.
We classify the simple quantum group modules with finite dimensional weight spaces when the quantum parameter $q$ is transcendental and the Lie algebra is not of type $G_2$. This is part $2$ of the story. The first part being Irreducible quantum group modules with finite dimensional weight spaces. I (arXiv:1504.07042). In that paper the classification is reduced to the classification of torsion free simple modules. In this paper we follow the procedures used by O. Mathieu to reduce the classification to the classification of infinite dimensional admissible simple highest weight modules. We the…
Some Rational Vertex Algebras
设$L((n-\tfrac 3 2)Λ_0)$，$n \in \Bbb N$是辛仿射李代数的不可约最高权模$L((n-\tfrac 3 2)Λ_0)$的顶点算子代数.我们找到了$L((n-\tfrac 3 2)Λ_0)$的不可约模的完备集，并证明了$\Cal O$范畴中$L((n-\tfrac 3 2)Λ_0)$的每个模都是完全可约的.
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