Standard monomials and invariant theory of arc spaces II: Symplectic group

TL;DR

This paper develops a standard monomial basis for the arc space of the Pfaffian variety and establishes invariant theory results for the symplectic group, extending classical theorems to arc spaces.

Contribution

It introduces a standard monomial basis for arc spaces of Pfaffian varieties and proves invariant theory theorems for the symplectic group in this context.

Findings

Constructed a standard monomial basis for the arc space of the Pfaffian variety.

Proved the arc space analogue of the fundamental theorems of invariant theory for the symplectic group.

Abstract

This is the second 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 Pfaffian variety over $K$. As an application, we prove the arc space analogue of the first and second fundamental theorems of invariant theory for the symplectic group.