THE DECOMPOSITION OF PERMUTATION MODULE FOR INFINITE CHEVALLEY GROUPS, II

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