Elliptic Double Affine Hecke Algebras

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dc.contributor.authorRains, Eric M.
dc.date.accessioned2025-12-22T09:26:51Z
dc.date.issued2020
dc.description.abstractWe give a construction of an affine Hecke algebra associated to any Coxeter group acting on an abelian variety by reflections; in the case of an affine Weyl group, the result is an elliptic analogue of the usual double affine Hecke algebra. As an application, we use a variant of the C~ₙ version of the construction to construct a flat noncommutative deformation of the nth symmetric power of any rational surface with a smooth anticanonical curve, and give a further construction which conjecturally is a corresponding deformation of the Hilbert scheme of points.
dc.description.sponsorshipThe author would particularly like to thank P. Etingof both for asking the original seed question (with an important assist from A. Okounkov!) and hosting the authors sabbatical at MIT (which the author would also like to thank, naturally) where much of the basic approach was worked out, with great assistance from conversations with not only Etingof but also (regarding various geometrical issues) B. Poonen. Thanks also go to T. Graber and E. Mantovan for helpful and encouraging conversations regarding the constructions of Section 2, as well as various general algebraic geometric questions, and to O. Chalykh for asking some fruitful questions about residue conditions. The author's work presented here was supported in part by grants from the National Science Foundation, DMS-1001645 and DMS-1500806.
dc.identifier.citationElliptic Double Affine Hecke Algebras. Eric M. Rains. SIGMA 16 (2020), 111, 133 pages
dc.identifier.doihttps://doi.org/10.3842/SIGMA.2020.111
dc.identifier.issn1815-0659
dc.identifier.other2020 Mathematics Subject Classification: 33D80; 39A70; 14A22
dc.identifier.otherarXiv:1709.02989
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/211009
dc.language.isoen
dc.publisherІнститут математики НАН України
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlier
dc.titleElliptic Double Affine Hecke Algebras
dc.typeArticle

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Symmetry, Integrability and Geometry: Methods and Applications, 2020, том 16, випуск за цей рік