首页/论文/2003.00462

arXiv 2003.004622020-03-01math.RTmath.RA

Admissible homomorphisms and equivariant relations between weighted projective lines

Jianmin Chen, Yanan Lin, Shiquan Ruan, Hongxia Zhang

备注：: 27pages

英文摘要：

The string group acts on the category of coherent sheaves over a weighted projective line by degree-shift actions. We study the equivariant equivalence relations induced by degree-shift actions between weighted projective lines. We prove that such an equivariant equivalence is characterized by an admissible homomorphism between the associated string groups. We classify all these equivariant equivalences for the weighted projective lines of domestic and tubular types.

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。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

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

相关论文

Rational extensions of the representation ring global functor and a splitting of global equivariant $K$-theory

We identify the group of homomorphisms $\operatorname{Hom}_{\mathcal{GF}}(F,\mathbf{RU}_{\mathbb Q})$ in the category of ($\operatorname{fin}$)-global functors to the rationalization of the unitary representation ring functor and deduce that the higher $\operatorname{Ext}$-groups $\operatorname{Ext}^n_{\mathcal{GF}}(F,\mathbf{RU}_{\mathbb Q})$, $n\geq 2$ have to vanish. This leads to a rational splitting of the ($\operatorname{fin}$)-global equivariant $K$-theory spectrum into a sum of Eilenberg-MacLane spectra. Interpreted in terms of cohomology theories, it means that the equivariant Chern c…

2018-01-22math.ATmath.RT

Endotrivial representations of finite groups and equivariant line bundles on the Brown complex

We relate endotrivial representations of a finite group in characteristic p to equivariant line bundles on the simplicial complex of non-trivial p-subgroups, by means of weak homomorphisms.

2015-11-02math.ATmath.GRmath.RT

Naturality of FHT isomorphism

Freed, Hopkins and Teleman constructed an isomorphism between twisted equivariant K-theory of compact Lie group $G$ and the "Verlinde ring" of the loop group of $G$. We call this isomorphism FHT isomorphism. However, it does not hold naturality with respect to group homomorphisms. We construct two "quasi functors" $t.e.K$ (a modification of twisted equivariant K-theory) and $RL$ (a modification of representation group of loop groups) so that FHT isomorphism is natural transformation between two "quasi functors" for tori, that is, we construct two "induced homomorphisms" of the "quasi functors"…

2015-02-12math.KTmath.RT

Restricting Representations from a Complex Group to a Real Form

Let $G$ be a complex connected reductive algebraic group and let $G_{\mathbb{R}}$ be a real form of $G$. We construct a sequence of functors $L_i\mathcal{R}$ from admissible (resp. finite-length) representations of $G$ to admissible (resp. finite-length) representations of $G_{\mathbb{R}}$. We establish many basic properties of these functors, including their behavior with respect to infinitesimal character, associated variety, and restriction to a maximal compact subgroup. We deduce that each $L_i\mathcal{R}$ takes unipotent representations of $G$ to unipotent representations of $G_{\mathbb{R…

2022-04-22math.RT

The based ring of the lowest two-sided cell of an affine Weyl group, III

We show that Lusztig's homomorphism from an affine Hecke algebra to the direct summand of its asymptotic Hecke algebra corresponding to the lowest two-sided cell is related to the homomorphism constructed by Chriss and Ginzburg using equivariant K-theory by a matrix over the representation ring of the associated algebraic group.

2015-06-01math.RT

Irreducible modules for equivariant map superalgebras and their extensions

Let $Γ$ be a group acting on a scheme $X$ and on a Lie superalgebra $\mathfrak{g}$, both defined over an algebraically closed field of characteristic zero $\Bbbk$. The corresponding equivariant map superalgebra $M(\mathfrak{g}, X)^Γ$ is the Lie superalgebra of equivariant regular maps from $X$ to $\mathfrak{g}$. In this paper we complete the classification of finite-dimensional irreducible $M(\mathfrak{g}, X)^Γ$-modules when $\mathfrak{g}$ is a finite-dimensional simple Lie superalgebra, $X$ is of finite type and $Γ$ is a finite abelian group acting freely on the rational points of $X$, by cla…

2021-05-17math.RT

更多相关论文收起更多论文

Elliptic Dynamical Quantum Groups and Equivariant Elliptic Cohomology

We define an elliptic version of the stable envelope of Maulik and Okounkov for the equivariant elliptic cohomology of cotangent bundles of Grassmannians. It is a version of the construction proposed by Aganagic and Okounkov and is based on weight functions and shuffle products. We construct an action of the dynamical elliptic quantum group associated with $\mathfrak{gl}_2$ on the equivariant elliptic cohomology of the union of cotangent bundles of Grassmannians. The generators of the elliptic quantum groups act as difference operators on sections of admissible bundles, a notion introduced in …

2018-12-21math.ATmath.RT

$p$进上半平面上等变线丛的整体截面

Global sections of equivariant line bundles on the $p$-adic upper half plane

该文研究$p$进上半平面上等变线丛整体截面的表示性质，证明其强对偶是拓扑长度至多2的可容许局部解析表示，给出不可约判据及相关覆盖函数空间对偶长度的显式公式。

2023-12-19math.NTmath.RT

关于斜 gentle 代数的同态与一般 $\tau$-正则不可约分支

On homomorphisms and generically $τ$-regular components for skewed-gentle algebras

Instituto de Matemáticas, UNAM（墨西哥国立自治大学数学研究所）

本文针对斜 gentle 代数，利用容许词给出同态基，推广 fringe 与 kiss，得到 E-不变量和 g-向量公式，并描述一般 τ-正则不可约分支。

2025-10-17math.RT

Twisted representation rings and Dirac induction

Extending ideas of twisted equivariant $K$-theory, we construct twisted versions of the representation rings for Lie superalgebras and Lie supergroups, built from projective $\Z_{2}$-graded representations with a given cocycle. We then investigate the pullback and pushforward maps on these representation rings (and their completions) associated to homomorphisms of Lie superalgebras and Lie supergroups. As an application, we consider the Lie supergroup $Π(T^{*}G)$, obtained by taking the cotangent bundle of a compact Lie group and reversing the parity of its fibers. An inclusion $H \hookrightar…

2004-10-25math.KTmath.RT

Differential invariants on symplectic spinors in contact projective geometry

We present a complete classification and the construction of $\mathrm{Mp}(2n+2,\mathbb{R})$-equivariant differential operators acting on the principal series representations, associated to the contact projective geometry on $\mathbb{RP}^{2n+1}$ and induced from the irreducible $\mathrm{Mp}(2n,\mathbb{R})$-submodules of the Segal-Shale-Weil representation twisted by a one-parameter family of characters. The proof is based on the classification of homomorphisms of generalized Verma modules for the Segal-Shale-Weil representation twisted by a one-parameter family of characters, together with a ge…

2017-03-21math-phmath.DGmath.FA

Lift of fractional D-brane charge to equivariant Cohomotopy theory

The lift of K-theoretic D-brane charge to M-theory was recently hypothesized to land in Cohomotopy cohomology theory. To further check this "Hypothesis H", here we explicitly compute the constraints on fractional D-brane charges at ADE-orientifold singularities imposed by the existence of lifts from equivariant K-theory to equivariant Cohomotopy theory, through Boardman's comparison homomorphism. We check the relevant cases and find that this condition singles out precisely those fractional D-brane charges which do not take irrational values, in any twisted sector. Given that the possibility o…

2019-11-10math-phmath.ATmath.GR

Nahm's equations, configuration spaces and flag manifolds

We give a positive answer to the Berry-Robbins problem for any compact Lie group G, i.e. we show the existence of a smooth W-equivariant map from the space of regular triples in a Cartan subalgebra to the flag manifold G/T. This map is constructed via solutions to Nahm's equations and it is compatible with the SO(3) action, where SO(3) acts on G/T via a regular homomorphism from SU(2) to G. We then generalize this picture to include an arbitrary homomorphism from SU(2) to G. This leads to an interesting geometrical picture which appears to be related to the Springer representation of the Weyl …

2001-10-10math.DGmath.RT

Graded Lie algebras and intersection cohomology

Let i be a homomorphism of the multiplicative group into a connected reductive algebraic group over C. Let G^i be the centralizer of the image i. Let LG be the Lie algebra of G and let L_nG (n integer) be the summands in the direct sum decomposition of LG determined by i. Assume that n is not zero. For any G^i-orbit O in L_nG and any irreducible G^i-equivariant local system L on O we consider the restriction of some cohomology sheaf of the intersection cohomology complex of the closure of O with coefficients in L to another orbit O' contained in the closure of O. For any irreducible G^i-equiva…

2006-05-11math.RT

Affine Braid group, JM elements and knot homology

In this paper we construct a homomorphism of the affine braid group $Br_n^{aff}$ in the convolution algebra of the equivariant matrix factorizations on the space $\overline{\mathcal{X}}_2=\mathfrak{b}_n\times GL_n\times\mathfrak{n}_n$ considered in the earlier paper of the authors. We explain that the pull-back on the stable part of the space $\overline{\mathcal{X}_2}$ intertwines with the natural homomorphism from the affine braid group $Br_n^{aff}$ to the finite braid group $Br_n$. This observation allows us derive a relation between the knot homology of the closure of $β\in Br_n$ and the kn…

2018-01-29math.GTmath.RT

Minimal Idempotents on Solvable Groups

In this paper, we begin to develop a theory of character sheaves on an affine algebraic group $G$ defined over an algebraically closed field $k$ of characteristic $p>0$ using the approach developed by Boyarchenko and Drinfeld for unipotent groups. Let $l$ be a prime different from $p$. Following Boyarchenko and Drinfeld, we define the notion of an admissible pair on $G$ and the corresponding idempotent in the $\overline{\mathbb{Q}_l}$-linear triangulated braided monoidal category $\mathscr{D}_G(G)$ of conjugation equivariant $\overline{\mathbb{Q}_l}$-complexes (under convolution with compact s…

2015-12-29math.RT

D^\dagger-affinity of formal models of flag varieties

Let G be the group of L-rational points of a connected split reductive group over a finite extension L of Q_p. We show that formal models of the algebraic flag variety X of G are D-affine for certain sheaves of arithmetic differential operators. We then introduce the category of coadmissible G-equivariant arithmetic D-modules on the system of formal models of X and prove that it is anti-equivalent to the category of admissible locally L-analytic G-representations with trivial infinitesimal character. We compute the equivariant arithmetic D-modules of certain classes of representations.

2017-09-17math.AGmath.NTmath.RT