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

Publication date: 23 March 2023

Abstract: 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.

Has companion code repository: https://github.com/zoltancoccyx/monoid-character-table

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