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On the action of Young subgroups on the complex of partitions

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Speaker: 
Gregory Arone
Affiliation: 
University of Virginia
Date: 
Fri, 19/06/2015 - 10:00 - 11:00
Location: 
MPIM Lecture Hall

The action of the symmetric group $S_n$ on the complex of partitions $P_n$ has received considerable attention. We study the restriction of this action to a Young subgroup of $S_n$. Let $G$ be a Young subgroup of $S_n$. Our main result is a $G$-equivariant decomposition of $P_n$. As an application, we describe the fixed point space $(P_n)^H$ in terms of subgroup posets, for every subgroup $H$ of $S_n$. For another application we obtain new information about the orbit space $(P_n)_G$, where $G$ is a Young subgroup.
 

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