Restriction of characters to subgroups of wreath products and basic sets\n for the symmetric group

2019/08/09 by Jean-Baptiste Gramain, Gramain, Jean-Baptiste, Adriana Marciuk +1
Mathematics · Neuroscience · #Finite Group Theory Research #Nuclear Receptors and Signaling

paper · pdf · doi:10.48550/arxiv.1908.03474

Abstract

In this paper, we give the decomposition into irreducible characters of the\nrestriction to the wreath product \ℤ_p-1 wr mathfrakS_w of any\nirreducible character of (\ℤ_p rtimes \ℤ_p-1) wr\n mathfrakS_w, where p is any odd prime, w \≥ 0 is an integer, and\n\ℤ_p and \ℤ_p-1 denote the cyclic groups of order p and\np-1 respectively. This answers the question of how to decompose the\nrestrictions to p-regular elements of irreducible characters of the symmetric\ngroup mathfrakS_n in the \ℤ-basis corresponding to the p-basic\nset of mathfrakS_n described by Brunat and Gramain in [1]. The result is\ngiven in terms of the Littlewood-Richardson coefficients for the symmetric\ngroup.\n

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