Permutation representations on invertible matrices

2004/11/24 by Yona Cherniavsky, Cherniavsky, Yona, Eli Bagno +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #math.CO #math.RT

paper · pdf · doi:10.48550/arxiv.math/0411556

arxiv created 2004/11/24 · arxiv updated 2009/12/01

Abstract

We discuss permutation representations which are obtained by the natural action of S_n × S_n on some special sets of invertible matrices, defined by simple combinatorial attributes. We decompose these representations into irreducibles. The multiplicities involved have a nice combinatorial interpretation. We also generalize known results on asymptotic behavior of the conjugacy representation of S_n.

Related

• Conjugacy in Permutation Representations of the Symmetric Group
• Permutation-Like Matrices
• Young's Natural Representations of S₄
• The conjugacy action of S_n and modules induced from centralisers
• How to write a permutation as a product of involutions (and why you might care)