Branching Rules for Specht Modules

2004/08/06 by Harald Ellers, John Murray, Ellers, Harald +1 · 1 citation
Mathematics · #20C20 #20C30 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:20C20 #msc:20C30

paper · pdf · doi:10.48550/arxiv.math/0408088

9 pages

arxiv created 2004/08/06 · arxiv updated 2009/12/01

Abstract

Let n be a positive integer and let Sigma_n be the symmetric group of degree n. Let S^lambda be the Specht module for Sigma_n corresponding to a partition lambda of n, defined over a field F of odd characteristic. We find the indecomposable components of the restriction of S^lambda to Sigma_n-1, and of the induction of S^lambda to Sigma_n+1. Namely, if b and B are block idempotents of FSigma_n-1 and FSigma_n+1 respectively, then the modules S^lambda b and S^lambda B are 0 or indecomposable. We give examples to show that the assumption that F has odd characteristic cannot be dropped.

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