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

Balthazar Charles (1)

1 LISN - Laboratoire Interdisciplinaire des Sciences du Numérique

In this paper we present an algorithm for e ciently counting xed points in a nite monoid M under a conjugacy-like action. We then prove a formula for the character table of M in terms of xed points and radical, which allows for the e ective computation of the character table of M over a eld of null characteristic, as well as its Cartan matrix, using a formula from [Thiéry '12], again in terms of xed points. We discuss the implementation details of the resulting algorithms and provide benchmarks of their performances.

Mots clés: Representation Theory (math.RT); FOS: Mathematics

Domaines: Théorie des représentations [math.RT]

Balthazar Charles. Computing character tables and Cartan matrices of finite monoids with fixed point counting. 2023. ⟨hal-04258708⟩