Work

Involutions in Coxeter groups

Year: 2025

Type: article

Abstract: We combinatorially characterize the number $$\textrm{cc}_2$$ 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 $$\textrm{cc}_2$$ cc 2 for all triangle groups and RACGs.

Source: Algebras and Representation Theory

DOI: 10.1007/s10468-025-10332-x

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

Institutions: Otto-von-Guericke-Universität Magdeburg, University of Lincoln, Heidelberg University, Heinrich Heine University Düsseldorf

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,490

Funder: Otto von Guericke University Magdeburg