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arXiv · 1608.06034

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 $(\mathrm{SL}(N),\mathrm{SO}(N))$ using Fourier transform, parabolic induction functor, and a nearby cycle sheaves construction due to Grinberg. As applications, we obtain results on cohomology of Hessenberg varieties and geometric constructions of irreducible representations of Hecke algebras of symmetric groups at $q=-1$.

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BibTeXRIS

Tsao-Hsien Chen, Kari Vilonen, Ting Xue. 2016-08-22. Springer correspondence for the split symmetric pair in type $A$. https://doi.org/10.1112/s0010437x18007443

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