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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2211.08123 |
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| _version_ | 1866914952968667136 |
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| author | Duro, Diego Martín |
| author_facet | Duro, Diego Martín |
| contents | In this paper, we study if, for a given simple module over a Hopf algebra, there exists a virtual module such that their tensor product is the regular module. This is related to a conjecture by Donald Knutson, later disproved and refined by Savitskii, stating that for every irreducible character of a finite group, there exists a virtual character such that their tensor product is the regular character. We also introduce the Knutson Index as a measure of Knutson's Conjecture failure, discuss its algebraic properties and present counter-examples to Savitskii's Conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_08123 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Knutson Index of the Representation Ring Duro, Diego Martín Representation Theory 20C15 (Primary) 57T05, 18D10 (Secondary) In this paper, we study if, for a given simple module over a Hopf algebra, there exists a virtual module such that their tensor product is the regular module. This is related to a conjecture by Donald Knutson, later disproved and refined by Savitskii, stating that for every irreducible character of a finite group, there exists a virtual character such that their tensor product is the regular character. We also introduce the Knutson Index as a measure of Knutson's Conjecture failure, discuss its algebraic properties and present counter-examples to Savitskii's Conjecture. |
| title | The Knutson Index of the Representation Ring |
| topic | Representation Theory 20C15 (Primary) 57T05, 18D10 (Secondary) |
| url | https://arxiv.org/abs/2211.08123 |