Involutions in Coxeter groups

IF 0.5 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2025-04-08 DOI:10.1007/s10468-025-10332-x

Anna Reimann, Yuri Santos Rego, Petra Schwer, Olga Varghese

引用次数: 0

Abstract

We combinatorially characterize the number \(\textrm{cc}_2\) of conjugacy classes of involutions in any Coxeter group in terms of higher rank odd graphs. This notion naturally generalizes the concept of odd graphs, used previously to count the number of conjugacy classes of reflections. Moreover, we provide formulae for finite and affine types, besides computing \(\textrm{cc}_2\) for all triangle groups and RACGs.

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考克斯特群体的内讧

我们用高阶奇图组合地刻画了任意Coxeter群中对合的共轭类的个数\(\textrm{cc}_2\)。这个概念很自然地推广了奇图的概念，奇图以前被用来计算反射的共轭类的数量。此外，除了计算所有三角形群和racg的\(\textrm{cc}_2\)外，我们还提供了有限型和仿射型的公式。

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.