Quasi-hereditary slim cyclotomic q-Schur algebras

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.(c) 2023 Elsevier B.V. All rights reserved.