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

Abstract

We prove a Littlewood-Richardson type formula for $(s_{\lambda /\mu },s_{\nu /\kappa }{)}_{t^k,t}$, 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.

11 pages, no figures

References in corpus (1)

• Vertex operators and 2-representations of quantum affine algebras