Work

Global representation ring and Knutson Index

Year: 2025

Type: article

Abstract: Global representation rings were discovered by Sarah Witherspoon in 1995 and the Knutson Index was introduced by the second author in 2022. In the present paper we introduce the Knutson Index for general commutative rings and study it for Burnside rings and global representation rings. We also introduce the global table of a finite group, that encompasses both the character table and the Burnside table of marks. We discuss what properties of a group can be recovered from its global table.

Source: Communications in Algebra

DOI: 10.1080/00927872.2025.2498055

Authors: Dylan Johnston, Diego Martín Duro, Dmitriy Rumynin

Institution: University of Warwick

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funders: Max-Planck-Gesellschaft, Engineering and Physical Sciences Research Council, Division of Mathematical Sciences, Heilbronn Institute for Mathematical Research

Awards: DTP 2020-2021 University of Warwick, Additional Funding for Mathematical Sciences: Heilbronn Institute for Mathematical Research