Representation Stability and Finite Orthogonal Groups

Arun S. Kannan; Zifan Wang

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Representation Stability and Finite Orthogonal Groups

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arxiv 2202.09910 v1 pith:W4DRW33K submitted 2022-02-20 math.RT math.CT

Zifan Wang , Arun S. Kannan This is my paper

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keywords groupsorthogonalstabilitycategoryfinitemathbfprovetheorem

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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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