Springer correspondence for the split symmetric pair in type $A$

  title={Springer correspondence for the split symmetric pair in type \$A\$},
  author={Tsao-Hsien Chen and Kari Vilonen and Ting Xue},
  journal={Compositio Mathematica},
  pages={2403 - 2425}
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… 
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