Kazhdan-Lusztig Algorithm for Whittaker Modules with Arbitrary Infinitesimal Characters

IF 0.5 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2023-10-16 DOI:10.1007/s10468-023-10222-0

Qixian Zhao

引用次数: 0

Abstract

Let \(\mathfrak {g}\) be a complex semisimple Lie algebra. We give a description of characters of irreducible Whittaker modules for \(\mathfrak {g}\) with any infinitesimal character, along with a Kazhdan-Lusztig algorithm for computing them. This generalizes Miličić-Soergel’s and Romanov’s results for integral infinitesimal characters. As a special case, we recover the non-integral Kazhdan-Lusztig conjecture for Verma modules.

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具有任意无穷小字符的惠特克模块的卡兹丹-卢兹蒂算法

让 \(\mathfrak {g}\) 是一个复半简单李代数。我们给出了具有任意无穷小特征的 \(\mathfrak {g}\) 的不可还原惠特克模块的特征描述，以及计算它们的卡兹丹-卢兹提格算法。这概括了米利契奇-索埃格尔和罗曼诺夫关于积分无穷小字符的结果。作为一个特例，我们恢复了维尔马模块的非积分卡兹丹-卢兹蒂格猜想。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Algebras and Representation Theory 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Algebras and Representation Theory features carefully refereed papers relating, in its broadest sense, to the structure and representation theory of algebras, including Lie algebras and superalgebras, rings of differential operators, group rings and algebras, C*-algebras and Hopf algebras, with particular emphasis on quantum groups. The journal contains high level, significant and original research papers, as well as expository survey papers written by specialists who present the state-of-the-art of well-defined subjects or subdomains. Occasionally, special issues on specific subjects are published as well, the latter allowing specialists and non-specialists to quickly get acquainted with new developments and topics within the field of rings, algebras and their applications.