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arXiv · 2202.09910

Representation Stability and Finite Orthogonal Groups

Zifan Wang·Arun S. Kannan
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Abstract

In this paper, we prove stability results about orthogonal groups over finite commutative rings where 2 is a unit. Inspired by Putman and Sam (2017), we construct a category $\mathbf{OrI}(R)$ and prove a Noetherianity theorem for the category of $\mathbf{OrI}(R)$-modules. This implies an asymptotic structure theorem for orthogonal groups. In addition, we show general homological stability theorems for orthogonal groups, with both untwisted and twisted coefficients, partially generalizing a result of Charney (1987).

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BibTeXRIS

Zifan Wang, Arun S. Kannan. 2022-02-20. Representation Stability and Finite Orthogonal Groups. https://doi.org/10.1007/s10468-023-10202-4

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