Invariant derivations and trace bounds
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916930334490624 |
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| author | Garibaldi, Skip Guralnick, Robert M. Rains, Eric M. |
| author_facet | Garibaldi, Skip Guralnick, Robert M. Rains, Eric M. |
| contents | About 20 years ago, J-P.~Serre announced a bound on the trace of elements of compact Lie groups under the adjoint representation together with related results, provided indications of his proofs, and invited a better proof. This note provides a new, general method for proving such bounds; uses that method to derive Serre's bounds; gives a second proof of Serre's announced results that (we learned) closely follows his original argument; and provides lower bounds for traces of other representations of compact Lie groups and for Brauer characters of finite groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_03101 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Invariant derivations and trace bounds Garibaldi, Skip Guralnick, Robert M. Rains, Eric M. Representation Theory Group Theory 22E47 (Primary), 22C05, 22G20 (Secondary) About 20 years ago, J-P.~Serre announced a bound on the trace of elements of compact Lie groups under the adjoint representation together with related results, provided indications of his proofs, and invited a better proof. This note provides a new, general method for proving such bounds; uses that method to derive Serre's bounds; gives a second proof of Serre's announced results that (we learned) closely follows his original argument; and provides lower bounds for traces of other representations of compact Lie groups and for Brauer characters of finite groups. |
| title | Invariant derivations and trace bounds |
| topic | Representation Theory Group Theory 22E47 (Primary), 22C05, 22G20 (Secondary) |
| url | https://arxiv.org/abs/2312.03101 |