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

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.

arXiv admin note: text overlap with arXiv:1902.02124

References in corpus (4)

• The Algebra of Conjugacy Classes in Symmetric Groups and Partial Permutations
• A general framework for the polynomiality property of the structure coefficients of double-class algebras
• $k$-partial permutations and the center of the wreath product ${\mathcal{S}}_k\wr {\mathcal{S}}_n$ algebra
• The center of the wreath product of symmetric groups algebra