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Involutions in Coxeter groups

We combinatorially characterize the number cc2 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 formu...

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Bibliographic Details
Main Authors: Reimann, Anna (Author) , Santos Rego, Yuri (Author) , Schwer, Petra (Author) , Varghese, Olga (Author)
Format: Article (Journal)
Language:English
Published: 8 April 2025
In: Algebras and representation theory
Year: 2025, Volume: 28, Issue: 2, Pages: 647-667
ISSN:1572-9079
DOI:10.1007/s10468-025-10332-x
Online Access:Verlag, kostenfrei, Volltext: https://doi.org/10.1007/s10468-025-10332-x
Verlag, kostenfrei, Volltext: https://link.springer.com/article/10.1007/s10468-025-10332-x
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Author Notes:Anna Reimann, Yuri Santos Rego, Petra Schwer, Olga Varghese
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Summary:We combinatorially characterize the number cc2 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 cc 2 for all triangle groups and RACGs.
Item Description:Veröffentlicht online: 8 April 2025
Gesehen am 16.03.2026
Physical Description:Online Resource
ISSN:1572-9079
DOI:10.1007/s10468-025-10332-x

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