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

The partition algebra and the Kronecker product (Extended Abstract)

We propose a new approach to study the Kronecker coefficients by using the Schur–Weyl duality between the symmetric group and the partition algebra

Simple modules for the partition algebra and monotone convergence of Kronecker coefficients

We construct bases of the simple modules for partition algebras which are indexed by paths in an alcove geometry. This allows us to give a concrete interpretation (and new proof) of the monotone convergence property for Kronecker coefficients using stratifications of the cell modules of the partition algebra

The partition algebra and the Kronecker coefficients

We propose a new approach to study the Kronecker coefficients by using the Schur-Weyl duality between the symmetric group and the partition algebra. We explain the limiting behaviour and associated bounds in the context of the partition algebra. Our analysis leads to a uniform description of the reduced Kronecker coefficients when one of the indexing partitions is a hook or a two-part partition

The blocks of the periplectic Brauer algebra in positive characteristic

We determine the blocks of the periplectic Brauer algebra over any field of odd characteristic