Beyond Rouquier partitions

We obtain closed formulas, in terms of Littlewood–Richardson coefficients, for the canonical basis elements of the Fock space representation of which are labeled by partitions having ‘locally small’ e-quotients and arbitrary e-cores. We further show that upon evaluation at v=1, this gives the corresponding decomposition numbers of the q-Schur algebra in characteristic l (where q is a primitive eth root of unity if l≠e and q=1 otherwise) whenever l is greater than the size of each constituent of the e-quotient.