A Littlewood-Richardson rule for the Macdonald inner product and bimodules over wreath products

摘要

We prove a Littlewood-Richardson type formula for (s(lambda/mu, s nu/kappa)tk,t), the pairing of two skew Schur functions in the Macdonald inner product at q = t(k) for positive integers k. This pairing counts graded decomposition numbers in the representation theory of wreath products of the algebra C[x]/x(k) and symmetric groups. (C) 2015 Published by Elsevier Inc.