Springer correspondence for the split symmetric pair in type A

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http://hdl.handle.net/10138/307127

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Chen , T-H , Vilonen , K & Xue , T 2018 , ' Springer correspondence for the split symmetric pair in type A ' , Compositio Mathematica , vol. 154 , no. 11 , pp. 2403-2425 . https://doi.org/10.1112/S0010437X18007443

Title: Springer correspondence for the split symmetric pair in type A
Author: Chen, Tsao-Hsien; Vilonen, Kari; Xue, Ting
Contributor: University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, Department of Mathematics and Statistics
Date: 2018-11
Language: eng
Number of pages: 23
Belongs to series: Compositio Mathematica
ISSN: 0010-437X
URI: http://hdl.handle.net/10138/307127
Abstract: In this paper we establish Springer correspondence for the symmetric pair (SL(N); 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.
Subject: Springer correspondence
nearby cycle sheaves
symmetric pairs
Hecke algebras
Hessenberg varieties
Fourier transform
PERVERSE SHEAVES
REPRESENTATIONS
ALGEBRAS
111 Mathematics
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