arXiv math/04125382004-12-30math.QA

Quantum conjugacy classes of simple matrix groups

A. Mudrov

备注：: 33 pages, AMS LaTeX

英文摘要：

Let $G$ be a simple complex classical group and $\g$ its Lie algebra. Let $\U_\hbar(\g)$ be the Drinfeld-Jimbo quantization of the universal enveloping algebra $\U(\g)$. We construct an explicit $\U_\hbar(\g)$-equivariant quantization of conjugacy classes of $G$ with Levi subgroups as the stabilizers.

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

非例外群的量子对称共轭类

Quantum symmetric conjugacy classes of non-exceptional groups

本文研究了经典矩阵群的量子对称共轭类，计算了其与量子稳定子群的一维表示。

2024-01-16math.QA

Quantization of borderline Levi conjugacy classes of orthogonal groups

We construct equivariant quantization of a special family of Levi conjugacy classes of the complex orthogonal group $SO(N)$, whose stabilizer contains a Cartesian factor $SO(2)\times SO(P)$, $1\leqslant P<N$, $P\equiv N \mod 2$.

2013-10-29math.QA

Non-Levi closed conjugacy classes of SO_q(N)

We construct explicit quantization of semisimple conjugacy classes of the complex orthogonal group SO(N) with non-Levi isotropy subgroups through an operator realization on highest weight modules of the quantum group U_q(so(N)).

2013-07-14math.QA

Conjugacy classes of p-cycles of type D in alternating groups

We classify the conjugacy classes of p-cycles of type D in alternating groups. This finishes the open cases in arXiv:0812.4628. We also determine all the subracks of those conjugacy classes which are not of type D.

2014-03-04math.QA

On pointed Hopf algebras associated to unmixed conjugacy classes in S_n

Let s in S_n be a product of disjoint cycles of the same length, C the conjugacy class of s and rho an irreducible representation of the isotropy group of s. We prove that either the Nichols algebra B(C, rho) is infinite-dimensional, or the braiding of the Yetter-Drinfeld module is negative.

2006-08-28math.QA

Representations of quantum conjugacy classes of orthosymplectic groups

Let $G$ be the complex symplectic or special orthogonal group and $\g$ its Lie algebra. With every point $x$ of the maximal torus $T\subset G$ we associate a highest weight module $M_x$ over the Drinfeld-Jimbo quantum group $U_q(\g)$ and a quantization of the conjugacy class of $x$ by operators in $\End(M_x)$. These quantizations are isomorphic for $x$ lying on the same orbit of the Weyl group, and $M_x$ support different representations of the same quantum conjugacy class.

2015-02-09math.QA

更多相关论文收起更多论文

Strictly transversal slices to conjugacy classes in algebraic groups

We show that for every conjugacy class O in a connected semisimple algebraic group G over a field of characteristic good for G one can find a special transversal slice S to the set of conjugacy classes in G such that O intersects S and dim O = codim S.

2017-09-19math.QAmath.RT

q-conjugacy classes in loop groups

We classify twisted conjugacy classes in loop groups, restricted to classical groups. The main tool we used is the so-called D_q module, an object which is related to vector bundles over elliptic curves.

2010-11-23math.GRmath.QA

Conjugacy classes of involutive automorphisms of the $C_{\ell}^{(1)}$ affine Kac-Moody algebras

The conjugacy classes of the involutive automorphisms of the affine Kac-Moody algebras \Cli\ for $\ell\geq 2$ are determined using the matrix formulation of automorphisms of an affine Kac-Moody algebra.

1994-10-03hep-thmath.QA

Conjugacy classes and centralizers for pivotal fusion categories

A criterion for Müger centralizer of a fusion subcategory of a braided non-degenerate fusion category is given. Along the way we extend some identities on the space of class functions of a fusion category introduced by Shimizu in \cite{scalg}. We also show that in a modular tensor category the product of two conjugacy class sums is a linear combination of conjugacy class sums with rational coefficients.

2019-04-03math.CTmath.QA

Twisted conjugacy classes, coadjoint orbits of loop groups and D-branes in the WZW-model

We show that untwisted respectively twisted conjugacy classes of a compact and simply connected Lie group which satisfy a certain integrality condition correspond naturally to irreducible highest weight representations of the corresponding affine Lie algebra. Along the way, review the classification of twisted conjugacy classes of a simply connected compact Lie group $G$ and give a description of their stabilizers in terms of the Dynkin diagram of the corresponding twisted affine Lie algebra.

2004-01-19hep-thmath.QA

2024-11-05math.CTmath.QAmath.RT