MULTIPLICITY-FREE REPRESENTATIONS OF THE PRINCIPAL A1-SUBGROUP IN A SIMPLE ALGEBRAIC GROUP

Let G be a simple algebraic group defined over an algebraically closed field k of characteristic p > 0. For p ≥ h, the Coxeter number of G, any regular unipotent element of G lies in an A1-subgroup of G; there is a unique G-conjugacy class of such subgroups and any member of this class is a so-called “principal A1-subgroup of G”. Here we classify all irreducible k G-modules whose restriction to a principal A1-subgroup of G has no repeated composition factors, extending the work of Liebeck, Seitz and Testerman which treated the same question when k is replaced by an algebraically closed field of characteristic zero.