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arXiv · 2107.05024

The algebra of conjugacy classes of the wreath product of a finite group with the symmetric group

Omar Tout
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Abstract

For a finite group $G,$ we define the concept of $G$-partial permutation and use it to show that the structure coefficients of the center of the wreath product $G\wr \mathcal{S}_n$ algebra are polynomials in $n$ with non-negative integer coefficients. Our main tool is a combinatorial algebra which projects onto the center of the group $G\wr \mathcal{S}_n$ algebra for every $n.$ This generalizes the Ivanov and Kerov method to prove the polynomiality property for the structure coefficients of the center of the symmetric group algebra.

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Omar Tout. 2021-07-11. The algebra of conjugacy classes of the wreath product of a finite group with the symmetric group. https://doi.org/10.1216/rmj.2023.53.561

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