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Mathematics > Rings and Algebras

Title: Global Representation Ring and Knutson Index

Authors: Dylan Johnston, Diego Martín Duro, Dmitriy Rumynin
(Submitted on 27 Mar 2024 (v1), last revised 3 May 2024 (this version, v3))
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.
Comments: Version 3: corrected issues in section 3, and other minor typos. 11 pages
Subjects: Rings and Algebras (math.RA); Group Theory (math.GR); Representation Theory (math.RT)
MSC classes: 19A22, 13E15, 20D20
Cite as: arXiv:2403.18498 [math.RA]
  (or arXiv:2403.18498v3 [math.RA] for this version)

Submission history

From: Dylan Johnston Mr [view email]
[v1] Wed, 27 Mar 2024 12:19:57 GMT (18kb)
[v2] Mon, 29 Apr 2024 11:03:03 GMT (19kb)
[v3] Fri, 3 May 2024 10:17:58 GMT (21kb)
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