An application of global Weyl modules of $\lie{sl}_{n+1}[t]$ to invariant theory

TL;DR

This paper connects the representation theory of global Weyl modules for {sl}_{n+1}[t] with classical invariant theory by identifying module components with polynomial ring subspaces.

Contribution

It introduces a novel approach linking global Weyl modules of current algebras to invariant theory problems.

Findings

Identification of {sl}_{n+1}-isotypical components with polynomial subspaces

Application of current algebra representation theory to classical invariant theory

New insights into the structure of global Weyl modules

Abstract

We identify $\lie{sl}_{n+1}$--isotypical components of global Weyl modules with natural subspaces in a polynomial ring, and then apply the representation theory of current algebras to classical problems in invariant theory.