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

Omar Tout*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (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 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.

Original languageEnglish
Pages (from-to)389-412
Number of pages24
JournalJournal of Algebraic Combinatorics
Volume53
Issue number2
DOIs
Publication statusPublished - Mar 2021
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics

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