The symmetric group action on rank-selected posets of injective words

Abstract

The symmetric group ${\mathfrak{S}}_n$ acts naturally on the poset of injective words over the alphabet $\{1,2,\dots ,n\}$. The induced representation on the homology of this poset has been computed by Reiner and Webb. We generalize their result by computing the representation of ${\mathfrak{S}}_n$ on the homology of all rank-selected subposets, in the sense of Stanley. A further generalization to the poset of $r$-colored injective words is given.

10 pages, minor changes

References in corpus (2)

• Representation stability for cohomology of configuration spaces in ${\mathbf{R}}^d$
• Spectral analysis of random-to-random Markov chains