On Weyl modules of cyclotomic qq-Schur algebras

We study on Weyl modules of cyclotomic $q$-Schur algebras. In particular, we give the character formula of the Weyl modules by using the Kostka numbers and some numbers which are computed by a generalization of Littlewood-Richardson rule. We also study corresponding symmetric functions. Finally, we give some simple applications to modular representations of cyclotomic $q$-Schur algebras.Comment: 28 page

The representation type of Ariki-Koike algebras and cyclotomic q-Schur algebras

We give a necessary and sufficient condition on parameters for Ariki-Koike algebras (resp. cyclotomic q-Schur algebras) to be of finite representation type.Comment: 23 pages, revised version (correcting some errors, containing some extended results), to appear in Adv. Mat