Modular representations of finite monoids of Lie type

Abstract

Let M be a finite monoid of Lie type of characteristic p. In this paper we compute the number of irreducible modular representations of M in characteristic p. To do this we combine the theory of semigroup representations, of Munn-Ponizovskii, with Richen's theory of modular representations of finite groups of Lie type. Each of these representations is determined by a certain triple ( I, J, χ) where lϵ2 s is a subset of the simple roots, Jϵ U(M) is J -class and χ:P 1 → F q ∗ is a character.