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arXiv · 2412.20909

Stiefel-Whitney Classes for Finite Symplectic Groups

Neha Malik·Steven Spallone
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Abstract

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 $\pi$ of $G$, in terms of character values of $\pi$ 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 $w_k(\pi)$.

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BibTeXRIS

Neha Malik, Steven Spallone. 2024-12-30. Stiefel-Whitney Classes for Finite Symplectic Groups. https://arxiv.org/abs/2412.20909

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