Small-dimensional representations of algebraic groups of type $A_l$

Álvaro L. Martínez

Published 2017-10-18Version 1

For $G$ an algebraic group of type $A_l$ over an algebraically closed field of characteristic $p$, we determine all irreducible rational representations of G in defining characteristic with dimensions $\le (l+1)^s$ for $s = 3, 4$, provided that $l > 18$, $l > 35$ respectively. We also give explicit descriptions of the corresponding modules for $s = 3$.