Semi-infinite Pl\"ucker relations and Weyl modules

TL;DR

This paper describes the semi-infinite Pl"ucker relations for type A flag varieties, explores their coordinate ring, and establishes an isomorphism with dual global Weyl modules, leading to a new character formula.

Contribution

It introduces the semi-infinite Pl"ucker relations and proves their connection to dual global Weyl modules, providing new insights into their structure and characters.

Findings

Established the semi-infinite Pl"ucker relations for type A.

Proved the isomorphism between the coordinate ring and dual global Weyl modules.

Derived a new character formula for these modules.

Abstract

The goal of this paper is twofold. First, we write down the semi-infinite Pl\"ucker relations, describing the Drinfeld-Pl\"ucker embedding of the (formal version of) semi-infinite flag varieties in type A. Second, we study the homogeneous coordinate ring, i.e. the quotient by the ideal generated by the semi-infinite Pl\"ucker relations. We establish the isomorphism with the algebra of dual global Weyl modules and derive a new character formula.