【56页精品】Quiver Schur algebras and q-Fock space

Abstract: We develop a graded version of the theory of cyclotomic q-Schur algebras, inthe spirit of the work of Brundan-Kleshchev on Hecke algebras and of Ariki onq-Schur algebras. As an application, we identify the coefficients of thecanonical basis on a higher level Fock space with q-analogues of thedecomposition numbers of cyclotomic q-Schur algebras.<..