Hessenberg varieties, intersections of quadrics, and the Springer correspondence

Chen, Tsao-Hsien; Vilonen, Kari; Xue, Ting

doi:10.1090/tran/7934

Hessenberg varieties, intersections of quadrics, and the Springer correspondence
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by Tsao-Hsien Chen, Kari Vilonen and Ting Xue PDF

Trans. Amer. Math. Soc. 373 (2020), 2427-2461 Request permission

Abstract:

In this paper we introduce a certain class of families of Hessenberg varieties arising from Springer theory for symmetric spaces. We study the geometry of those Hessenberg varieties and investigate their monodromy representations in detail using the geometry of complete intersections of quadrics. We obtain decompositions of these monodromy representations into irreducibles and compute the Fourier transforms of the IC complexes associated to these irreducible representations. The results of the paper refine (part of) the Springer correspondece for the split symmetric pair $(SL(N),SO(N))$ in [Compos. Math. 154 (2018), pp. 2403–2425].

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