Sydney University Algebra Seminar

    University of Sydney

    School of Mathematics and Statistics

    Algebra Seminar

    Andrew Mathas
    University of Sydney

    Morita equivalences of Ariki-Koike algebra.

    Friday 22nd October, 12-1pm, Carslaw 375.

    An Ariki-Koike algebra H is an algebra attached to the complex reflection group W of type G(r,1,n); that is, W is the wreath product of a cyclic group of order r and a symmetric group of degree n. The algebra H depends upon r+1 parameters q, u1, ...,ur.

    The aim of this talk is to show that up to Morita equivalence H can be replaced by a direct sum of tensor products of "smaller" Ariki-Koike algebras, each with a parameter set which consists of a single q-orbit; special cases of this result were obtained previously by Dipper-James, Du-Rui and Ariki. This result is not only interesting but was the key reduction in the classification of the simple modules of the Ariki-Koike algebras. Other applications will also be discussed.

    This is joint work with Richard Dipper (Stuttgart).