University of Sydney

    School of Mathematics and Statistics

    Algebra Seminar

    Hebing Rui
    University of NSW

    Ariki-Koike algebras with semisimple bottoms

    Friday 17th July, 12-1pm, Carslaw 273.

    Let H be the Ariki-Koike algebra over an integral domain R containing elements q, q-1 u1, ... , um. In this talk, we introduce the characteristic polynomial fm, r(q, u1, ... ,um) in R and prove that the categories of H-modules and

    \oplus_{\lambda\in \Lambda(m, r)} H(S_\lambda)-modules
    are Morita equivalent if fm, r is a unit. This generalizes Theorem (4.17) of Dipper-James's paper "Representations of Hecke algebras of type B_n" (J. Algebra, Vol 146, 454-481). Therefore, the q-Schur^m algebra is Morita equivalent to the direct sum of tensor products of certain q-Schur algebras. Some applications are obtained.

    This is the joint work with J. Du.