Modular representations of finite monoids of Lie type

AbstractLet 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 lϵ2s is a subset of the simple roots, JϵU(M) is J-class and χ:P1 → Fq∗ is a character