Noetherianity of some degree two twisted commutative algebras

TL;DR

This paper proves that certain degree two twisted commutative algebras are noetherian, introducing new methods and highlighting their significance in the context of stable representation theory of classical groups.

Contribution

It establishes the noetherian property for a new class of degree two twisted commutative algebras using novel proof techniques.

Findings

Certain degree two twisted commutative algebras are noetherian.

New proof methods for establishing noetherianity.

Connections to stable representation theory of classical groups.

Abstract

In recent years, researchers have discovered various large algebraic structures that have surprising finiteness properties, such as FI-modules and Delta-modules. In this paper, we add another example to the growing list: we show that certain degree two twisted commutative algebras are noetherian. This example appears to have some fundamental differences from previous examples, and is therefore especially interesting. Reflective of this, our proof introduces new methods for establishing noetherianity that are likely to be applicable in other situations. The algebras considered in this paper are closely related to the stable representation theory of classical groups, which is one source of motivation for their study.