Semi-infinite Pl\"ucker relations and arcs over toric degeneration

TL;DR

This paper investigates the algebra of Weyl modules in types A and C using arcs over toric degenerations, providing explicit generators, relations, and a basis construction.

Contribution

It introduces a novel approach combining arcs over toric degenerations with functional realization to analyze Weyl module algebras in types A and C.

Findings

Computed generators and relations of the algebra.

Constructed an explicit basis for the algebra.

Enhanced understanding of Weyl modules in types A and C.

Abstract

We study the algebra of Weyl modules in types $A$ and $C$ using the methods of arcs over toric degenerations and functional realization of dual space. We compute the generators and relations of this algebra and construct its basis.