Global Representation Ring and Knutson Index
Rings and Algebras
2025-04-14 v6 Group Theory
Representation Theory
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.
Cite
@article{arxiv.2403.18498,
title = {Global Representation Ring and Knutson Index},
author = {Dylan Johnston and Diego Martín Duro and Dmitriy Rumynin},
journal= {arXiv preprint arXiv:2403.18498},
year = {2025}
}
Comments
Version 6: Minor typos corrected for journal submission