The spectrum of a twisted commutative algebra

Abstract

A twisted commutative algebra is (for us) a commutative ‐algebra equipped with an action of the infinite general linear group. In such algebras, the “‐prime” ideals assume the duties fulfilled by prime ideals in ordinary commutative algebra, and so it is crucial to understand them. Unfortunately, distinct ‐primes can have the same radical, which obstructs one from studying them geometrically. We show that this problem can be eliminated by working with super vector spaces: doing so provides enough geometry to distinguish ‐primes. This yields an effective method for analyzing ‐primes.