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

TL;DR

This paper provides explicit formulas and multiplicities for the decomposition of induced characters from the centralizer of an n-cycle in the symmetric group on 2n elements, advancing understanding of character theory in symmetric groups.

Contribution

It introduces explicit formulas for character multiplicities in the induced representation from the centralizer of an n-cycle in S_{2n}.

Findings

Derived explicit multiplicity formulas for induced characters.

Provided detailed decomposition of characters in symmetric groups.

Enhanced understanding of centralizer-induced character structures.

Abstract

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