Slim cyclotomic q-Schur algebras
背景资料：A slim cyclotomic q-Schur algebra is a endomorphism algebra of certain permutation module over the cyclotomic Hecke algebra ( or the Ariki-Koike algebra ). In this talk, We will construct a new basis for a slim cyclotomic q-Schur algebra via symmetric polynomials in Jucys-Murphy operators of the cyclotomic Hecke algebra. We show that this basis, labelled by matrices, is not the double coset basis when the cyclotomic Hecke algebra has type $B$, but coincides with the double coset basis for the corresponding group algebra. This talk is based on joint work with Bangming Deng and Jie Du..