Papers › Computing character tables and Cartan matrices of finite monoids with fixed point counting

Computing character tables and Cartan matrices of finite monoids with fixed point counting

23 Mar 2023arXiv:2303.13647links table onlyarchive 2025-07-28

Balthazar Charles

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In this paper we present an algorithm for efficiently counting fixed points in a finite monoid M under a conjugacy-like action. We then prove a formula for the character table of M in terms of fixed points and radical, which allows for the effective computation of the character table of M over a field of null characteristic, as well as its Cartan matrix, using a formula from [Thi\'ery '12], again in terms of fixed points. We discuss the implementation details of the resulting algorithms and provide benchmarks of their performances.

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