Another runner removal theorem for v-decomposition numbers of Iwahori–Hecke algebras and q-Schur algebras

Let denote the Fock space representation of the quantum group . The ‘v-decomposition numbers’ are the coefficients when the canonical basis for this representation is expanded in terms of the basis of partitions, and the evaluations at v=1 of these polynomials give the decomposition numbers for Iwahori–Hecke algebras and q-Schur algebras over . James and Mathas have proved a theorem which relates v-decomposition numbers for different values of e, by adding empty runners to the abacus displays for the labelling partitions. Here we prove a similar theorem, which involves adding ‘full’ runners to these abacus displays.