Sydney University Algebra Seminar

    University of Sydney

    School of Mathematics and Statistics

    Algebra Seminar

    Andrew Mathas
    University of Sydney

    Tilting modules for cyclotomic Schur algebras.

    Friday August 3rd, 12-1pm, Carslaw 375.

    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 GLn(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.