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].
Bibliographical noteFunding Information:
Received by the editors June 10, 2018, and, in revised form, June 14, 2019. 2010 Mathematics Subject Classification. Primary 14M10, 17B08, 22E60. The first author was supported in part by the AMS-Simons travel grant and the NSF grant DMS-1702337. The second author was partially supported by the ARC grants DP150103525 and DP180101445, the Academy of Finland, NSF grant DMS-1402928, the Humboldt Foundation, and the Simons Foundation. The third author was partially supported by the ARC grants DP150103525, DE160100975 and the Academy of Finland. 1IC=intersection cohomology.
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