Representation Stability and Finite Orthogonal Groups

Autor:	Wang, Zifan, Kannan, Arun S.
Rok vydání:	2022
Předmět:	Mathematics - Representation Theory Mathematics - Category Theory 16P40 18A25 18Gxx 20J05
Druh dokumentu:	Working Paper
DOI:	10.1007/s10468-023-10202-4
Popis:	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). Comment: 21 pages, 0 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2202.09910 Zobrazit plný text záznamu View this record from Arxiv