Springer correspondence for the split symmetric pair in type A

Tsao Hsien Chen; Kari Vilonen; Ting Xue

doi:10.1112/S0010437X18007443

Springer correspondence for the split symmetric pair in type A

Tsao Hsien Chen, Kari Vilonen, Ting Xue

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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)
Pages (from-to)	2403-2425
Number of pages	23
Journal	Compositio Mathematica
Volume	154
Issue number	11
DOIs	https://doi.org/10.1112/S0010437X18007443
State	Published - Nov 1 2018
Externally published	Yes

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Publisher Copyright:
© 2018 The Author.

Keywords

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

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AU - Vilonen, Kari

AU - Xue, Ting

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KW - Fourier transform

KW - Hecke algebras

KW - Hessenberg varieties

KW - Springer correspondence

KW - nearby cycle sheaves

KW - symmetric pairs

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Springer correspondence for the split symmetric pair in type A

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