Topological noetherianity for algebraic representations of infinite rank classical groups

TL;DR

This paper extends the concept of topological noetherianity from polynomial representations of infinite-dimensional general linear groups to algebraic representations of other infinite rank classical groups, broadening the understanding of their algebraic structure.

Contribution

It generalizes Draisma's result on topological noetherianity from $ extbf{GL}_{ ext{infinity}}$ to a wider class of infinite rank classical groups.

Findings

Polynomial representations of $ extbf{GL}_{ ext{infinity}}$ are topologically noetherian.

Algebraic representations of other infinite rank classical groups are also topologically noetherian.

Abstract

Draisma recently proved that polynomial representations of $\mathbf{GL}_{\infty}$ are topologically noetherian. We generalize this result to algebraic representations of infinite rank classical groups.