Quasi-hereditary quotients of finite Chevalley groups and Frobenius kernels

De Visscher, M. (2005). Quasi-hereditary quotients of finite Chevalley groups and Frobenius kernels. The Quarterly Journal of Mathematics, 56(1), pp. 111-121. doi: 10.1093/qmath/hah025

Abstract

Let G be a semisimple connected simply connected linear algebraic group over an algebraically closed field k of characteristic p > 0. Denote by Gn its nth Frobenius kernel and by G(pn) its finite subgroup of Fpn-rational points. In this paper we find quotients of the algebra Un = k[Gn]* and of the group algebra kG(pn) whose module category is equivalent to a (highest weight) subcategory of the category of rational G-modules.