The decomposition of permutation module for infinite Chevalley groups, II

Abstract

Let $\bf G$ be a connected reductive algebraic group over an algebraically closed field $\Bbbk$ and ${\bf B}$ be an Borel subgroup of ${\bf G}$. In this paper we completely determine the composition factors of the permutation module $\mathbb{F}[{\bf G}/{\bf B}]$ for any field $\mathbb{F}$.