Representation Stability and Finite Orthogonal Groups

Author(s)
Kannan, Arun S.; Wang, Zifan
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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.
Date issued
2023-03-29
URI
https://hdl.handle.net/1721.1/150331
Department
Massachusetts Institute of Technology. Department of Mathematics
Publisher
Springer Netherlands
Citation
Kannan, Arun S. and Wang, Zifan. 2023. "Representation Stability and Finite Orthogonal Groups."
Version: Final published version
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