论文标题
表示稳定性和有限正交组
Representation Stability and Finite Orthogonal Groups
论文作者
论文摘要
在本文中，我们证明了关于2个单位的有限交换环的正交组的稳定性结果。受Putman和Sam（2017）的启发，我们构建了一个类别$ \ Mathbf {ori}（r）$，并证明了$ \ Mathbf {ori}（ori}（r）$ - 模块的类别的Noetherianity定理。这意味着正交组的渐近结构定理。此外，我们还展示了正交组的一般同源稳定性定理，既有扭曲和扭曲的系数，又部分概括了Charney（1987）的结果。
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).
