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Springer correspondence for the split symmetric pair in type
$A$
- Part of
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- Journal:
- Compositio Mathematica / Volume 154 / Issue 11 / November 2018
- Published online by Cambridge University Press:
- 11 October 2018, pp. 2403-2425
- Print publication:
- November 2018
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- Article
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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.
