k-partial permutations and the center of the wreath product Sk≀ Sn algebra

Omar Tout

doi:10.1007/s10801-019-00934-2

k-partial permutations and the center of the wreath product S_k≀ S_n algebra

Omar Tout^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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 S_k≀ S_n algebra are polynomials in n with nonnegative integer coefficients. We use a universal algebra I∞k, which projects on the center Z(C[S_k≀ S_n]) for each n. We show that I∞k is isomorphic to the algebra of shifted symmetric functions on many alphabets.

Original language	English
Pages (from-to)	389-412
Number of pages	24
Journal	Journal of Algebraic Combinatorics
Volume	53
Issue number	2
DOIs	https://doi.org/10.1007/s10801-019-00934-2
Publication status	Published - Mar 2021

Keywords

Character theory
Shifted symmetric functions
Structure coefficients
Wreath product of symmetric groups
k-partial permutations

ASJC Scopus subject areas

Algebra and Number Theory
Discrete Mathematics and Combinatorics

Access to Document

10.1007/s10801-019-00934-2

Cite this

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title = "k-partial permutations and the center of the wreath product Sk≀ Sn 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 Sk≀ Sn algebra are polynomials in n with nonnegative integer coefficients. We use a universal algebra I∞k, which projects on the center Z(C[Sk≀ Sn]) for each n. We show that I∞k is isomorphic to the algebra of shifted symmetric functions on many alphabets.",

keywords = "Character theory, Shifted symmetric functions, Structure coefficients, Wreath product of symmetric groups, k-partial permutations",

author = "Omar Tout",

note = "Funding Information: This research is supported by Narodowe Centrum Nauki, Grant Number 2017/26/A/ST1/00189. Publisher Copyright: {\textcopyright} 2020, The Author(s).",

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AB - 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 Sk≀ Sn algebra are polynomials in n with nonnegative integer coefficients. We use a universal algebra I∞k, which projects on the center Z(C[Sk≀ Sn]) for each n. We show that I∞k is isomorphic to the algebra of shifted symmetric functions on many alphabets.

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