Nilpotent varieties in symmetric spaces and twisted affine Schubert 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.

In this arXiv version, we correct a calculation mistake in the end of the proof of Lemma 2.2 and delete a wrong comment in the paragraph above Theorem 5.4 (published version)