ALVIS–CURTIS DUALITY ON LOWERCASE q-SCHUR AND HECKE ALGEBRAS

摘要

We show that for a finite reductive group tensoring with a quotient of the complex inducing the Alvis–Curtis character duality induces a self-derived equivalence on a quotient of the group algebra. In the case of general linear groups, this equivalence realizes an equivalence between derived categories of q-Schur algebras. Furthermore, in the latter case, multiplication of the quotient complex by an idempotent induces an isomorphism with the two-sided q-analogue of the Coxeter complex.