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 language | English (US) |
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Pages (from-to) | 2403-2425 |
Number of pages | 23 |
Journal | Compositio Mathematica |
Volume | 154 |
Issue number | 11 |
DOIs | |
State | Published - Nov 1 2018 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2018 The Author.
Keywords
- Fourier transform
- Hecke algebras
- Hessenberg varieties
- Springer correspondence
- nearby cycle sheaves
- symmetric pairs