Springer correspondence for the split symmetric pair in type A

Tsao Hsien Chen, Kari Vilonen, Ting Xue

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

In this paper we establish Springer correspondence for the symmetric pair 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 . Conversely, we see that the irreducible representations of Hecke algebras of symmetric groups at arise in geometry.

Original languageEnglish (US)
Pages (from-to)2403-2425
Number of pages23
JournalCompositio Mathematica
Volume154
Issue number11
DOIs
StatePublished - Nov 1 2018
Externally publishedYes

Bibliographical note

Funding Information:
Chen Tsao-Hsien Vilonen Kari Xue Ting Department of Mathematics , University of Chicago , Chicago 60637 , USA email chenth@math.uchicago.edu School of Mathematics and Statistics , University of Melbourne , VIC 3010 , Australia email kari.vilonen@unimelb.edu.au Department of Mathematics and Statistics , University of Helsinki , Helsinki 00014 , Finland School of Mathematics and Statistics , University of Melbourne , VIC 3010 , Australia email ting.xue@unimelb.edu.au Department of Mathematics and Statistics , University of Helsinki , Helsinki 00014 , Finland The first author was supported in part by the AMS-Simons travel grant and the NSF grant DMS-1702337. The second author was supported in part by the ARC grants DP150103525 and DP180101445, the Academy of Finland, the Humboldt Foundation, the Simons Foundation, and the NSF grant DMS-1402928. The third author was supported in part by the ARC grants DE160100975, DP150103525 and the Academy of Finland. 11 10 2018 11 2018 154 11 2403 2425 28 01 2017 25 05 2018 © The Authors 2018  2018 The Authors 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.

Publisher Copyright:
© 2018 The Author.

Keywords

  • Fourier transform
  • Hecke algebras
  • Hessenberg varieties
  • Springer correspondence
  • nearby cycle sheaves
  • symmetric pairs

Fingerprint

Dive into the research topics of 'Springer correspondence for the split symmetric pair in type A'. Together they form a unique fingerprint.

Cite this