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Unramified affine Springer fibers and isospectral Hilbert schemes

Kivinen, Oscar (2020) Unramified affine Springer fibers and isospectral Hilbert schemes. Selecta Mathematica - New Series, 26 (4). Art. No. 61. ISSN 1022-1824. https://resolver.caltech.edu/CaltechAUTHORS:20200914-134006155

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Abstract

For any connected reductive group G over C, we revisit Goresky–Kottwitz–MacPherson’s description of the torus equivariant Borel–Moore homology of affine Springer fibers Sp_γ ⊂ Gr_G, where γ = zt^d and z is a regular semisimple element in the Lie algebra of G. In the case G = GL_n, we relate the equivariant cohomology of Sp_γ to Haiman’s work on the isospectral Hilbert scheme of points on the plane. We also explain the connection to the HOMFLY homology of (n, dn)-torus links, and formulate a conjecture describing the homology of the Hilbert scheme of points on the curve {x^n = y^(dn)}.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s00029-020-00587-1DOIArticle
https://arxiv.org/abs/1808.02278arXivDiscussion Paper
Additional Information:© 2020 Springer. Published 10 August 2020. I would like to thank Erik Carlsson, Victor Ginzburg, Eugene Gorsky, Mark Haiman, Matthew Hogancamp, Alexei Oblomkov, Hiraku Nakajima, Peng Shan, Eric Vasserot and Zhiwei Yun for interesting discussions on the subject. Special thanks to Roman Bezrukavnikov for suggesting the reference [18]. Additionally, I would like to thank the MSRI for hospitality, for most of the work was completed there during Spring 2018. This research was supported by the NSF grants DMS-1700814 and DMS-1559338, as well as the Vilho, Yrjö and Kalle Väisälä foundation of the Finnish Academy of Science and Letters.
Funders:
Funding AgencyGrant Number
NSFDMS-1700814
NSFDMS-1559338
Vilho FoundationUNSPECIFIED
Yrjö FoundationUNSPECIFIED
Kalle Väisälä FoundationUNSPECIFIED
Finnish Academy of Science and LettersUNSPECIFIED
Issue or Number:4
Record Number:CaltechAUTHORS:20200914-134006155
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200914-134006155
Official Citation:Kivinen, O. Unramified affine Springer fibers and isospectral Hilbert schemes. Sel. Math. New Ser. 26, 61 (2020). https://doi.org/10.1007/s00029-020-00587-1
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:105379
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:14 Sep 2020 22:07
Last Modified:14 Sep 2020 22:07

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