The decomposition of permutation module for infinite Chevalley groups, II

TL;DR

This paper fully determines the composition factors of permutation modules for infinite Chevalley groups over algebraically closed fields, advancing understanding of their representation theory.

Contribution

It provides a complete classification of the composition factors of permutation modules for any field, extending previous partial results.

Findings

Explicit description of composition factors for permutation modules

Generalization to all fields

Advancement in representation theory of Chevalley groups

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 $\mathbb{F}$.