题目：Slim Cyclotomic Q-Schur Algebras
报告人：杜杰 教授 （新南威尔士大学）
摘要：Slim cyclotomic q-Schur algebras were first introduced by Z. Lin and H. Rui, as centralizer subalgebras of Dipper-James-Mathas’ cyclotomic q-Schur algebras. Recent developments allow us to take the investigation to a new level. First, by using the matrix labelling of C. Mak for certain double cosets, we may construct an integral basis, simpler than the cellular basis, for these algebras. Second, the introduction of the Lusztig type form for quantum affine gl_n by Q. Fu and myself allows us to establish the cyclotomic Schur-Weyl duality at the integral level. Finally, when q is not a root of unity, we obtain a classification of irreducible representations. I will also mention some problems and conjectures. This is joint work with B. Deng and G. Yang.
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