April 2023 THE ALGEBRA OF CONJUGACY CLASSES OF THE WREATH PRODUCT OF A FINITE GROUP WITH THE SYMMETRIC GROUP
Omar Tout
Rocky Mountain J. Math. 53(2): 561-577 (April 2023). DOI: 10.1216/rmj.2023.53.561

Abstract

Let G be a finite group. In this expository paper, we provide a detailed proof of the polynomiality property of the structure coefficients of the center of the wreath product G𝒮n algebra. Our main tool is a universal combinatorial algebra which projects onto the center of the group G𝒮n algebra for every n. We show that this universal algebra is isomorphic to the algebra of shifted symmetric functions on |G| alphabets.

Citation

Download Citation

Omar Tout. "THE ALGEBRA OF CONJUGACY CLASSES OF THE WREATH PRODUCT OF A FINITE GROUP WITH THE SYMMETRIC GROUP." Rocky Mountain J. Math. 53 (2) 561 - 577, April 2023. https://doi.org/10.1216/rmj.2023.53.561

Information

Received: 20 August 2021; Revised: 2 October 2022; Accepted: 20 January 2023; Published: April 2023
First available in Project Euclid: 20 June 2023

MathSciNet: MR4604774
zbMATH: 07725155
Digital Object Identifier: 10.1216/rmj.2023.53.561

Subjects:
Primary: 05E05 , 05E10 , 20C30
Secondary: 20E22

Keywords: character theory , partial permutations , shifted symmetric functions , structure coefficients , wreath product

Rights: Copyright © 2023 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
17 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

Vol.53 • No. 2 • April 2023
Back to Top