Global Representation Ring and Knutson Index
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917982123327488 |
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| author | Johnston, Dylan Duro, Diego Martín Rumynin, Dmitriy |
| author_facet | Johnston, Dylan Duro, Diego Martín Rumynin, Dmitriy |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18498 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global Representation Ring and Knutson Index Johnston, Dylan Duro, Diego Martín Rumynin, Dmitriy Rings and Algebras Group Theory Representation Theory 19A22, 13E15, 20D20 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. |
| title | Global Representation Ring and Knutson Index |
| topic | Rings and Algebras Group Theory Representation Theory 19A22, 13E15, 20D20 |
| url | https://arxiv.org/abs/2403.18498 |