Low-dimensional irreducible rational representations of classical algebraic groups

Álvaro L. Martínez

paper

Low-dimensional irreducible rational representations of classical algebraic groups

arXiv:1811.07019

Abstract

Let $G$ be an algebraic group of classical type of rank $l$ over an algebraically closed field $K$ of characteristic $p$ . We list and determine the dimensions of all irreducible $K G$ -modules $L$ with $dim L < (4 l + 1)$ if $G$ is of type $A_{l}$ , and with $dim L < 16 (4 l)$ , if $G$ is of type $B_{l}$ , $C_{l}$ or $D_{l}$ .