Representation Stability and Finite Orthogonal Groups
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10468_2023_Article_10202.pdf
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421.81 KB
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Author(s)
Kannan, Arun S.
Wang, Zifan
Date Issued
March 29, 2023
Publisher
Springer Netherlands
Citation
Kannan, Arun S. and Wang, Zifan. 2023. "Representation Stability and Finite Orthogonal Groups."
Version
Final published version
Abstract
Abstract
In this paper, we prove homological stability results about orthogonal groups over finite commutative rings where 2 is a unit. Inspired by Putman and Sam (2017), we construct a category OrI(R) and prove a local Noetherianity theorem for the category of 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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/s10468-023-10202-4
