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

Abstract

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