A Frobenius-Type Formula for Compact Lie Groups
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912074417831936 |
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| author | Garge, Shripad Sharma, Uday Bhaskar |
| author_facet | Garge, Shripad Sharma, Uday Bhaskar |
| contents | Let $G$ be a group and $α: G \times G \to G$ denote the commutator map. In the case of finite groups, Frobenius gave the formula to compute the cardinalities of the fibres $α^{-1}(g)$ in terms of the character values $χ(g)$ for irreducible characters $χ$ of $G$. We generalise this formula to compact Lie groups. Further, we connect this generalised formula to the commutator probability of the concerned groups. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_12282 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Frobenius-Type Formula for Compact Lie Groups Garge, Shripad Sharma, Uday Bhaskar Group Theory 22C05, 20F24 Let $G$ be a group and $α: G \times G \to G$ denote the commutator map. In the case of finite groups, Frobenius gave the formula to compute the cardinalities of the fibres $α^{-1}(g)$ in terms of the character values $χ(g)$ for irreducible characters $χ$ of $G$. We generalise this formula to compact Lie groups. Further, we connect this generalised formula to the commutator probability of the concerned groups. |
| title | A Frobenius-Type Formula for Compact Lie Groups |
| topic | Group Theory 22C05, 20F24 |
| url | https://arxiv.org/abs/2410.12282 |