Quasi-hereditary slim cyclotomic q-Schur algebras

Abstract

Slim cyclotomic q-Schur algebras are certain centralizer subalgebras of cyclotomic q-Schur algebras in the sense of Dipper, James and Mathas, including q-Schur algebras of type A and C as examples. In the present paper we provide a sufficient condition for a slim cyclotomic q-Schur algebra Sm(n,r) to be quasi-hereditary. More precisely, it is shown that Sm(n,r) is quasi-hereditary if the cyclotomic Hecke algebra has a semisimple bottom. Moreover, we prove that Sm(1,r) is quasi-hereditary if and only if the cyclotomic Hecke algebra has a semisimple bottom. In the case where m=n=r=2 and q=±1, we prove that this condition is also necessary.