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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2306.12408 |
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| _version_ | 1866911156708311040 |
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| author | Duro, Diego Martín |
| author_facet | Duro, Diego Martín |
| contents | In this paper, we introduce the generalised Knutson Index and compute it for the special linear groups and projective special linear groups of degree two by computing the lowest common multiple of the degrees of their irreducible representations. We also classify all alternating and symmetric groups such that the lowest common multiple of the degrees of their irreducible representations equals the order groups, which yields a lower bound on the generalised Knutson Indices of these groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_12408 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Arithmetic Properties of Character Degrees and the Generalised Knutson Index Duro, Diego Martín Representation Theory In this paper, we introduce the generalised Knutson Index and compute it for the special linear groups and projective special linear groups of degree two by computing the lowest common multiple of the degrees of their irreducible representations. We also classify all alternating and symmetric groups such that the lowest common multiple of the degrees of their irreducible representations equals the order groups, which yields a lower bound on the generalised Knutson Indices of these groups. |
| title | Arithmetic Properties of Character Degrees and the Generalised Knutson Index |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2306.12408 |