Pl\:ucker relations and spherical varieties: application to model varieties

TL;DR

This paper introduces a framework for simplifying the equations of spherical varieties by relating them to Grassmannians, and applies it to model varieties of types A, B, and C, establishing a standard monomial theory.

Contribution

It develops a general reduction framework for spherical varieties and provides a new standard monomial theory for model varieties of types A, B, and C.

Findings

Framework reduces equations of spherical varieties to Grassmannians

Standard monomial theory established for model varieties

Applicable to types A, B, and C spherical varieties

Abstract

A general framework for the reduction of the equations defining classes of spherical varieties to (maybe infinite dimensional) grassmannians is proposed. This is applied to model varieties of type A, B and C; in particular a standard monomial theory for these varieties is presented.