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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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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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.
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 2427-2461
  • MSC (2010): Primary 14M10, 17B08, 22E60
  • DOI: https://doi.org/10.1090/tran/7934
  • MathSciNet review: 4069224