A remark on irreducible modules for finite Lie-type groups
Let G be a finite group of Lie type, P a parabolic subgroup of G with unipotent radical M, K an algebraically closed field of prime characteristic, and V an irreducible KG-module. Using algebraic group methods, \textit{S. D. Smith} [J. Algebra 75, 286-289 (1982; Zbl 0496.20030)] has shown that if G is not of twisted type, then \(C_ V(M)\) is an irreducible module for P, so is a Levi complement. The author uses two results from the representation theory of groups of Lie type to construct a shorter and more general proof of this fact, one that establishes the result for G of twisted as well as of untwisted type.
scientific article; zbMATH DE number 3973163