Degenerate flag varieties and Schubert varieties: a characteristic free approach

TL;DR

This paper demonstrates that degenerate flag varieties in types A and C are isomorphic to Schubert varieties across all characteristics by analyzing PBW filtrations and Demazure modules, providing a characteristic-free perspective.

Contribution

It introduces a characteristic-free approach linking degenerate flag varieties to Schubert varieties via PBW filtrations and Demazure modules.

Findings

Degenerate flag varieties are isomorphic to Schubert varieties in any characteristic.

The associated graded modules are realized as Demazure modules for doubled rank groups.

The approach applies uniformly across different characteristics.

Abstract

We consider the PBW filtrations over the integers of the irreducible highest weight modules in type A and C. We show that the associated graded modules can be realized as Demazure modules for group schemes of the same type and doubled rank. We deduce that the corresponding degenerate flag varieties are isomorphic to Schubert varieties in any characteristic.