Refined knot invariants and Hilbert schemes

Eugene Gorsky; Andrei Neguţ

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arXiv · 1304.3328

Refined knot invariants and Hilbert schemes

Eugene Gorsky·Andrei Neguţ

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Abstract

We consider the construction of refined Chern-Simons torus knot invariants by M. Aganagic and S. Shakirov from the DAHA viewpoint of I. Cherednik. We give a proof of Cherednik's conjecture on the stabilization of superpolynomials, and then use the results of O. Schiffmann and E. Vasserot to relate knot invariants to the Hilbert scheme of points on the plane. Then we use the methods of the second author to compute these invariants explicitly in the uncolored case. We also propose a conjecture relating these constructions to the rational Cherednik algebra, as in the work of the first author, A. Oblomkov, J. Rasmussen and V. Shende. Among the combinatorial consequences of this work is a statement of the m/n shuffle conjecture.

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BibTeX RIS

Eugene Gorsky, Andrei Neguţ. 2013-04-11. Refined knot invariants and Hilbert schemes. https://arxiv.org/abs/1304.3328

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