Slim cyclotomic q-Schur algebras

Abstract We construct a new basis for a slim cyclotomic q -Schur algebra S m ( n , r ) via symmetric polynomials in Jucys–Murphy operators of the cyclotomic Hecke algebra H m ( r ) . We show that this basis, labelled by matrices, is not the double coset basis when H m ( r ) is the Hecke algebra of a Coxeter group, but coincides with the double coset basis for the corresponding group algebra, the Hecke algebra at q = 1 . As further applications, we then discuss the cyclotomic Schur–Weyl duality at the integral level. This also includes a category equivalence and a classification of simple objects.