A branching rule for partition complexes

Abstract

Let $S_n$ be the symmetric group, and let $Y$ be a Young subgroup of $S_n$. Let ${\Pi }_n$ be the complex of partitions of $\{1,\dots ,n\}$. Our main result is a $Y$-equivariant decomposition of ${\Pi }_n$. As an application, we obtain new information about the quotient space of $|{\Pi }_n|$ by a Young subgroup.

Added a remark about related work of Lukas Brantner. Made a few minor changes

Cited by in corpus (1)

• Symmetric products and subgroup lattices