Tuesday, June 26, 14:00, 7.527

Sam Thelin, Generalised Schur algebras and representation
type.

Abstract:

The classical Schur algebra S_{K}(n,d) can be described
as (M_{n}(K)^{⊗d})^{Sd} -
the subalgebra of the tensor product of d copies of
M_{n}(K) invariant under the natural permutation action of
the symmetric group on d letters. The representation
type of the classical Schur algebras was determined by Doty, Erdmann, Martin
and Nakano. In recent work, Evseev and Kleshchev introduced the generalised
Schur algebra S^{A}(n, d):=
(M_{n}(A)^{⊗d})^{Sd}
for A an arbitrary finite-dimensional K-algebra. We
determine the representation type of S^{A}(n, d) in the case
where A is a semisimple algebra and
describe some work in progress in the direction of deciding the
representation type for more general algebras A.