Standard monomials and invariant theory for arc spaces I: general linear group

Andrew R. Linshaw, Bailin Song

Published 2021-08-16Version 1

This is the first in a series of papers on standard monomial theory and invariant theory of arc spaces. For any algebraically closed field $K$, we construct a standard monomial basis for the arc space of the determinantal variety over $K$. As an application, we prove the arc space analogue of the first and second fundamental theorems of invariant theory for the general linear group.