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 $\mathbb{k}$ and $\mathbf{B}$ be an 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 $\mathbb{F}$.

16 pages, accepted by Nagoya Mathematical Journal