Pure and Applied Mathematics Quarterly

Volume 20 (2024)

Number 1

Special Issue dedicated to Corrado De Concini

Guest Editors: Alberto De Sole, Nicoletta Cantarini, and Andrea Maffei

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

Pages: 139 – 169

DOI: https://dx.doi.org/10.4310/PAMQ.2024.v20.n1.a5

Authors

Rocco Chirivì (Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Università del Salento, Lecce, Italy)

Xin Fang (Lehrstuhl für Algebra und Darstellungstheorie, RWTH Aachen University, Aachen, Germany)

Peter Littelmann (Department Mathematik/Informatik, Universität zu Köln, Germany)

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.

Keywords

Seshadri stratification, Schubert variety, standard monomial theory, LS-path

2010 Mathematics Subject Classification

13F50, 14M15, 14M25

Full Text (PDF format)

Received 18 July 2022

Accepted 6 April 2023

Published 26 March 2024