A note on the tensor product of restricted simple modules for algebraic groups

Let G be a semisimple simply connected algebraic group over an algebraically closed field of positive characteristic p. Denote by G1 its first Frobenius kernel. In this note, we determine for which group G the restriction to G1 of any indecomposable G-summand of the tensor product of any two restricted simple G-modules remains indecomposable

Quasi-hereditary quotients of finite Chevalley groups and Frobenius kernels

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

The blocks of the Brauer algebra in characteristic zero

We determine the blocks of the Brauer algebra in characteristic zero. We also give information on the submodule structure of standard modules for this algebra

A geometric characterisation of the blocks of the Brauer algebra

We give a geometric description of the blocks of the Brauer algebra $B_n(\delta)$ in characteristic zero as orbits of the Weyl group of type $D_n$. We show how the corresponding affine Weyl group controls the representation theory of the Brauer algebra in positive characteristic, with orbits corresponding to unions of blocks.Comment: 26 pages, 24 figure