Degenerate flag varieties and Schubert varieties: a characteristic free approach

Giovanni Cerulli Irelli, Martina Lanini and Peter Littelmann

Vol. 284 (2016), No. 2, 283–308

DOI: 10.2140/pjm.2016.284.283

Abstract

We consider the PBW filtrations over $\mathbb{Z}$ of the irreducible highest weight modules in type $A_n$ and $C_n$. 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.

Keywords

Schubert varieties, degenerate flag varieties, Demazure modules

Mathematical Subject Classification 2010

Primary: 17B10

Secondary: 17B35, 16S30, 20G40, 14N15

Milestones

Received: 16 November 2015

Revised: 6 May 2016

Accepted: 7 May 2016

Published: 30 August 2016