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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.20909 |
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| _version_ | 1866908709833146368 |
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| author | Malik, Neha Spallone, Steven |
| author_facet | Malik, Neha Spallone, Steven |
| contents | Let $q$ be an odd prime power, and $G=\text{Sp}(2n,q)$ the finite symplectic group. We give an expression for the total Stiefel-Whitney Classes (SWCs) for orthogonal representations $π$ of $G$, in terms of character values of $π$ at elements of order $2$. We give "universal formulas'' for the fourth and eighth SWCs. For $n=2$, we compute the subring of the mod $2$ cohomology generated by the SWCs $w_k(π)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20909 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stiefel-Whitney Classes for Finite Symplectic Groups Malik, Neha Spallone, Steven Representation Theory Algebraic Topology 20G40, 55R40 Let $q$ be an odd prime power, and $G=\text{Sp}(2n,q)$ the finite symplectic group. We give an expression for the total Stiefel-Whitney Classes (SWCs) for orthogonal representations $π$ of $G$, in terms of character values of $π$ at elements of order $2$. We give "universal formulas'' for the fourth and eighth SWCs. For $n=2$, we compute the subring of the mod $2$ cohomology generated by the SWCs $w_k(π)$. |
| title | Stiefel-Whitney Classes for Finite Symplectic Groups |
| topic | Representation Theory Algebraic Topology 20G40, 55R40 |
| url | https://arxiv.org/abs/2412.20909 |