OIST Representation Theory Seminar
Speaker: Chun-Ju Lai, Academia Sinica
Title: Quasi-hereditary covers, Hecke subalgebras and quantum wreath product
Abstract: The Hecke algebra is in general not quasi-hereditary, meaning that its module category is not a highest weight category; while it admits a quasi-hereditary cover via category O for certain rational Cherednik algebras due to Ginzburg-Guay-Opdam-Rouquier. It was proved in type A that this category O can be realized using q-Schur algebra, but this realization problem remains open beyond types A/B/C. An essential step for type D is to study Hu's Hecke subalgebra, which deforms from a wreath product that is not a Coxeter group. In this talk, I'll talk about a new theory allowing us to take the ``quantum wreath product'' of an algebra by a Hecke algebra. Our wreath product produces the Ariki-Koike algebra as a special case, as well as new ``Hecke algebras'' of wreath products between symmetric groups. We expect them to play a role in answering the realization problem for complex reflection groups. This is a joint work with Dan Nakano and Ziqing Xiang.