表示稳定性与有限正交群

Pub Date : 2023-03-29 DOI:10.1007/s10468-023-10202-4

Arun S. Kannan, Zifan Wang

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引用次数: 0

摘要

在本文中，我们证明了有限交换环上正交群的同调稳定性结果，其中 2 是一个单位。受 Putman 和 Sam (2017) 的启发，我们构建了一个 OrI(R) 范畴，并证明了 OrI(R) 模块范畴的局部 Noetherianity 定理。这意味着正交群的渐近结构定理。此外，我们还展示了具有非扭曲系数和扭曲系数的正交群的一般同调稳定性定理。

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Representation Stability and Finite Orthogonal Groups

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.

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