Decomposing induced characters of the centralizer of an n-cycle in the symmetric group on 2n elements

Ricci, Joseph

doi:10.2140/involve.2013.6.221

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Decomposing induced characters of the centralizer of an $n$-cycle in the symmetric group on $2n$ elements

Joseph Ricci

Vol. 6 (2013), No. 2, 221–232

DOI: 10.2140/involve.2013.6.221

Abstract

We give explicit multiplicities and formulas for multiplicities of the characters appearing in the decomposition of the induced character ${Ind}_{C_{S_{2 n}} (σ)}^{S_{2 n}} 1_{C}$ , where $σ$ is an $n$ -cycle, $C_{S_{2 n}} “ (σ)$ is the centralizer of $σ$ in $S_{2 n}$ , and $1_{C} “$ is the trivial character on $C_{S_{2 n}} (σ)$ .

Keywords

representation theory, symmetric group, character theory

Mathematical Subject Classification 2010

Primary: 20C30

Secondary: 20C15

Milestones

Received: 3 January 2012

Revised: 3 February 2012

Accepted: 17 July 2012

Published: 1 September 2013

Communicated by Nigel Boston

Authors

Joseph Ricci
Mathematics Department University at Buffalo, SUNY Buffalo, NY 14260 United States

Vol. 6, No. 2, 2013