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

摘要

Let F denote the Fock space representation of the quantum group U nu((Sl(e)) over cap). The 'nu-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 nu = 1 of these polynomials give the decomposition numbers for Iwahori-Hecke algebras and q-Schur algebras over C. James and Mathas have proved a theorem which relates nu-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. (c) 2007 Elsevier Inc. All rights reserved.