Hessenberg varieties, intersections of quadrics, and the Springer correspondence
Algebraic Geometry
2020-06-23 v2 Representation Theory
Abstract
In this paper we introduce a certain class of families of Hessenberg varieties arising from Springer theory for symmetric spaces. We study the geometry of those Hessenberg varieties and investigate their monodromy representations in detail using the geometry of complete intersections of quadrics. We obtain decompositions of these monodromy representations into irreducibles and compute the Fourier transforms of the IC complexes associated to these irreducible representations. The results of the paper refine (part of) the Springer correspondece for the split symmetric pair (SL(N),SO(N)) in [CVX2].
Keywords
Cite
@article{arxiv.1511.00617,
title = {Hessenberg varieties, intersections of quadrics, and the Springer correspondence},
author = {Tsao-Hsien Chen and Kari Vilonen and Ting Xue},
journal= {arXiv preprint arXiv:1511.00617},
year = {2020}
}
Comments
Final version