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Title: Springer correspondence for the split symmetric pair in type
In this paper we establish Springer correspondence for the symmetric pair $$(\text{SL}(N),\text{SO}(N))$$ using Fourier transform, parabolic induction functor, and a nearby cycle sheaf construction. As an application of our results we see that the cohomology of Hessenberg varieties can be expressed in terms of irreducible representations of Hecke algebras of symmetric groups at $q=-1$ . Conversely, we see that the irreducible representations of Hecke algebras of symmetric groups at $q=-1$ arise in geometry.  more » « less
Award ID(s):
1702337 2022303
PAR ID:
10198237
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Compositio Mathematica
Volume:
154
Issue:
11
ISSN:
0010-437X
Page Range / eLocation ID:
2403 to 2425
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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