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Permutation representations on invertible matrices

Yona Cherniavsky·Eli Bagno
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Abstract

We discuss permutation representations which are obtained by the natural action of $S_n \times S_n$ 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 $S_n$.

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Yona Cherniavsky, Eli Bagno. 2004-11-24. Permutation representations on invertible matrices. https://arxiv.org/abs/math/0411556

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