Nilpotent varieties in symmetric spaces and twisted affine Schubert varieties

TL;DR

This paper explores the geometric relationship between Schubert varieties in twisted affine Grassmannians and nilpotent varieties in symmetric spaces, extending previous results and providing new insights into classical symmetric space structures.

Contribution

It extends Achar-Henderson's results to the twisted setting and applies these findings to the geometry of order 2 nilpotent varieties in classical symmetric spaces.

Findings

Extended results of Achar-Henderson to twisted affine Grassmannians.

Established geometric relations between Schubert and nilpotent varieties in symmetric spaces.

Provided applications to the structure of order 2 nilpotent varieties.

Abstract

We relate the geometry of Schubert varieties in twisted affine Grassmannian and the nilpotent varieties in symmetric spaces. This extends some results of Achar-Henderson in the twisted setting. We also get some applications to the geometry of the order 2 nilpotent varieties in certain classical symmetric spaces.