Springer correspondence for the split symmetric pair in type $A

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...

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Bibliographic Details
Published in:	Compositio mathematica 2018-11, Vol.154 (11), p.2403-2425, Article 2403
Main Authors:	Chen, Tsao-Hsien, Vilonen, Kari, Xue, Ting
Format:	Article
Language:	eng ; fre
Subjects:	Fourier transforms Grants Group theory Homology Orbits Representations
Online Access:	Get full text
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Summary:	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.
ISSN:	0010-437X 1570-5846