
School of Mathematics and Statistics
Hebing Rui University of NSW
ArikiKoike algebras with semisimple bottoms
Friday 17th July, 121pm, Carslaw 273.
Let H be the ArikiKoike algebra over an integral domain
R containing elements q, q^{1} u_{1}, ... , u_{m}.
In this talk, we introduce the characteristic polynomial
f_{m, r}(q, u_{1}, ... ,u_{m}) in R and prove that the
categories of Hmodules and
\oplus_{\lambda\in \Lambda(m, r)} H(S_\lambda)modules
are Morita equivalent if f_{m, r} is a unit. This generalizes
Theorem (4.17) of DipperJames's paper "Representations of Hecke algebras of
type B_n" (J. Algebra, Vol 146, 454481). Therefore, the
qSchur^m algebra is Morita equivalent to the direct sum
of tensor products of certain qSchur algebras. Some applications
are obtained.
This is the joint work with J. Du.
