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arXiv · 1902.02124

$k$-partial permutations and the center of the wreath product $\mathcal{S}_k\wr \mathcal{S}_n$ algebra

Omar Tout
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Abstract

We generalize the concept of partial permutations of Ivanov and Kerov and introduce $k$-partial permutations. This allows us to show that the structure coefficients of the center of the wreath product $\mathcal{S}_k\wr \mathcal{S}_n$ algebra are polynomials in $n$ with non-negative integer coefficients. We use a universal algebra $\mathcal{I}_\infty^k$ which projects on the center $Z(\mathbb{C}[\mathcal{S}_k\wr \mathcal{S}_n])$ for each $n.$ We show that $\mathcal{I}_\infty^k$ is isomorphic to the algebra of shifted symmetric functions on many alphabets.

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Omar Tout. 2019-02-06. $k$-partial permutations and the center of the wreath product $\mathcal{S}_k\wr \mathcal{S}_n$ algebra. https://doi.org/10.1007/s10801-019-00934-2

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