Sym-Noetherianity for powers of GL-varieties

Abstract

Much recent literature concerns finiteness properties of infinite-dimensional algebraic varieties equipped with an action of the infinite symmetric group, or of the infinite general linear group. In this paper, we study a common generalisation in which the product of both groups acts on infinite-dimensional spaces, and we show that these spaces are topologically Noetherian with respect to this action.

References in corpus (6)

• FI-modules and stability for representations of symmetric groups
• Noetherianity of some degree two twisted commutative algebras
• FI- and OI-modules with varying coefficients
• The geometry of polynomial representations
• Finiteness properties of congruence classes of infinite matrices
• Sp-equivariant modules over polynomial rings in infinitely many variables