Involutions and the Gelfand character

Abstract

The Gelfand representation of ${\mathcal{S}}_n$ is the multiplicity-free direct sum of the irreducible representations of ${\mathcal{S}}_n$. In this paper, we use a result of Adin, Postnikov, and Roichman to find a recursive generating function for the Gelfand character. In order to find this generating function, we investigate descents of so-called $\lambda$-unimodal involutions.

References in corpus (1)

• A note on the number of $k$-roots in $S_n$