Affine Matsuki correspondence for sheaves
Representation Theory
2023-11-14 v2 Algebraic Geometry
Abstract
We lift the affine Matsuki correspondence between real and symmetric loop group orbits in affine Grassmannians to an equivalence of derived categories of sheaves. In analogy with the finite-dimensional setting, our arguments depend upon the Morse theory of energy functions obtained from symmetrizations of coadjoint orbits. The additional fusion structures of the affine setting lead to further equivalences with Schubert constructible derived categories of sheaves on real affine Grassmannians.
Cite
@article{arxiv.1805.06514,
title = {Affine Matsuki correspondence for sheaves},
author = {Tsao-Hsien Chen and David Nadler},
journal= {arXiv preprint arXiv:1805.06514},
year = {2023}
}
Comments
Add a new section (Section 9) on compatibility with Hecke actions