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

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.

References in corpus (3)

• A general framework for the polynomiality property of the structure coefficients of double-class algebras
• A Frobenius formula for the structure coefficients of double-class algebras of Gelfand pairs
• Polynomialité des coefficients de structure des algèbres de doubles-classes

Cited by in corpus (2)

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