Seshadri stratifications and Schubert varieties: a geometric construction of a standard monomial theory

TL;DR

This paper develops a geometric approach to standard monomial theory for Schubert varieties using Seshadri stratifications and LS-path combinatorics, enhancing the general theory with flexible linearizations.

Contribution

It introduces a new geometric construction of standard monomial theory for Schubert varieties based on Seshadri stratifications and LS-path formulas, with improved generality.

Findings

Constructed a standard monomial theory for Schubert varieties.

Utilized Seshadri stratifications and LS-path formulas.

Enhanced the general theory with flexible linearizations.

Abstract

A standard monomial theory for Schubert varieties is constructed exploiting (1) the geometry of the Seshadri stratifications of Schubert varieties by their Schubert subvarieties and (2) the combinatorial LS-path character formula for Demazure modules. The general theory of Seshadri stratifications is improved by using arbitrary linearization of the partial order and by weakening the definition of balanced stratification.