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Transactions of the American Mathematical Society

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Hessenberg varieties, intersections of quadrics, and the Springer correspondence


Authors: Tsao-Hsien Chen, Kari Vilonen and Ting Xue
Journal: Trans. Amer. Math. Soc. 373 (2020), 2427-2461
MSC (2010): Primary 14M10, 17B08, 22E60
DOI: https://doi.org/10.1090/tran/7934
Published electronically: January 7, 2020
MathSciNet review: 4069224
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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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Additional Information

Tsao-Hsien Chen
Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
Address at time of publication: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email: chenth@umn.edu

Kari Vilonen
Affiliation: School of Mathematics and Statistics, University of Melbourne, Australia; and Department of Mathematics and Statistics, University of Helsinki, Finland
MR Author ID: 178620
Email: kari.vilonen@unimelb.edu.au

Ting Xue
Affiliation: School of Mathematics and Statistics, University of Melbourne, Australia; and Department of Mathematics and Statistics, University of Helsinki, Finland
MR Author ID: 779365
Email: ting.xue@unimelb.edu.au

Received by editor(s): June 10, 2018
Received by editor(s) in revised form: June 14, 2019
Published electronically: January 7, 2020
Additional Notes: 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.
Article copyright: © Copyright 2019 American Mathematical Society