A branching rule for partition complexes

2015/08/20 by Gregory Arone, Arone, Gregory
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.1508.05086

Abstract

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

Citations

• Partition Complexes, Tits Buildings and Symmetric Products

Related

• The action of Young subgroups on the partition complex
• Some branching laws for symmetric spaces
• Reconstructing Partitions from their Multisets of k-Minors
• On Measures on Partitions Arising in Harmonic Analysis for Linear and Projective Characters of the Infinite Symmetric Group
• Identifying Self-Conjugate Partitions