Speaker: Chun-Ju Lai, UGA
On q-Schur algebras of type B via coordinate coalgebras
Abstract: In this talk we investigate the q-Schur algebras of type B that were constructed earlier in the study of the quantum symmetric pairs (QSP). We introduce a coordinate algebra type construction that allows us to realize these q-Schur algebras as the duals of the dth graded components of certain graded coalgebras. We generalized a Morita equivalence theorem due to Dipper and James to the q-Schur algebras, and it in turn demonstrates that the representation theory of the QSP coideal subalgebras reduces to the q-Schur algebra of type A. This enables one to address the questions of cellularity, quasi-hereditariness and representation type of these algebras. It is also shown that these algebras realize the 1-faithful quasi-hereditary covers of the Hecke algebras of type B, and hence provide an identification of the category O of the rational Cherednik algebras of type B and the corresponding KZ functors. This is a joint work with Nakano and Xiang.