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

2013/09/18 by Erik Carlsson, Carlsson, Erik, Anthony M. Licata +1
Mathematics · #05E05 #16D90 #81R50 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:05E05 #msc:16D90 #msc:81R50

paper · pdf · doi:10.48550/arxiv.1309.4510

11 pages, no figures

arxiv created 2013/09/18 · arxiv updated 2013/09/19

Abstract

We prove a Littlewood-Richardson type formula for (s_λ/μ,s_ν/κ)_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.

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