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2018 DAHA and plane curve singularities
Ivan Cherednik, Ian Philipp
Algebr. Geom. Topol. 18(1): 333-385 (2018). DOI: 10.2140/agt.2018.18.333

Abstract

We suggest a relatively simple and totally geometric conjectural description of uncolored daha superpolynomials of arbitrary algebraic knots (conjecturally coinciding with the reduced stable Khovanov–Rozansky polynomials) via the flagged Jacobian factors (new objects) of the corresponding unibranch plane curve singularities. This generalizes the Cherednik–Danilenko conjecture on the Betti numbers of Jacobian factors, the Gorsky combinatorial conjectural interpretation of superpolynomials of torus knots and that by Gorsky and Mazin for their constant term. The paper mainly focuses on nontorus algebraic knots. A connection with the conjecture due to Oblomkov, Rasmussen and Shende is possible, but our approach is different. A motivic version of our conjecture is related to p –adic orbital A –type integrals for anisotropic centralizers.

Citation

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Ivan Cherednik. Ian Philipp. "DAHA and plane curve singularities." Algebr. Geom. Topol. 18 (1) 333 - 385, 2018. https://doi.org/10.2140/agt.2018.18.333

Information

Received: 28 October 2016; Revised: 15 May 2017; Accepted: 12 June 2017; Published: 2018
First available in Project Euclid: 1 February 2018

zbMATH: 06828007
MathSciNet: MR3748246
Digital Object Identifier: 10.2140/agt.2018.18.333

Subjects:
Primary: 14H50, 17B45, 20C08, 20F36, 33D52, 57M25
Secondary: 17B22, 22E50, 22E57, 30F10, 33D80

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 1 • 2018
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