Algebra Seminar

The cyclotomic Schur algebras are endomorphism algebras of a direct sum of ``permutation like'' modules for the Ariki-Koike algebras: they include as special cases the q-Schur algebras of Dipper and James. These algebras were introduced partly to provide a new tool for studying the Ariki-Koike algebras and partly in the hope that they might generalize the beautiful Dipper-James theory which shows that the q-Schur algebras completely determine the modular representation theory of the GL_n(q) in non-defining characteristic.

As yet there are no known (non type A) connections between the representation theory of the cyclotomic Schur algebras and that of the finite groups of Lie type; nonetheless the representation theory of these algebras is both rich and beautiful. For example, they are quasi-hereditary algebras and Jantzen's sum formula generalizes to this setting. In this talk I will survey the representation theory of the cyclotomic Schur algebras culminating with a description of their tilting modules.