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Exceptional knot homology

Elliot, Ross and Gukov, Sergei (2016) Exceptional knot homology. Journal of Knot Theory and its Ramifications, 25 (3). Art. No. 1640003. ISSN 0218-2165. http://resolver.caltech.edu/CaltechAUTHORS:20160425-090534476

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Abstract

The goal of this paper is twofold. First, we find a natural home for the double affine Hecke algebras (DAHA) in the physics of BPS states. Second, we introduce new invariants of torus knots and links called hyperpolynomials that address the “problem of negative coefficients” often encountered in DAHA-based approaches to homological invariants of torus knots and links. Furthermore, from the physics of BPS states and the spectra of singularities associated with Landau–Ginzburg potentials, we also describe a rich structure of differentials that act on homological knot invariants for exceptional groups and uniquely determine the latter for torus knots.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1142/S0218216516400034DOIArticle
http://www.worldscientific.com/doi/10.1142/S0218216516400034PublisherArticle
http://arxiv.org/abs/1505.01635arXivDiscussion Paper
Additional Information:© 2016 World Scientific Publishing Co Pte Ltd. Received: 31 July 2015; Accepted: 21 December 2015; Published: 1 February 2016. Our special thanks go to Ivan Cherednik, who provided the formulas for DAHA-Jones polynomials and participated in the development of many ideas contained herein. Without his contributions, this work would not be possible. We would also like to thank J. Adams, M. Aschbacher, D. Bar-Natan, P. Cvitanović , W.A. de Graaf, A. Gabrielov, and S. Morrison for helpful discussions. The work of S.G. is funded in part by the DOE Grant DE-SC0011632 and the Walter Burke Institute for Theoretical Physics. The work of R.E. is partially supported by a Troesh Family Graduate Fellowship 2014-15.
Group:Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Troesh Family Graduate Fellowship 2014-15UNSPECIFIED
Subject Keywords:BPS states; double affine Hecke algebras; superpolynomials; knot homology; quantum invariants; exceptional Lie algebras; singularity theory; Landau–Ginzburg potential
Classification Code:AMSC: 57M27, 81T30, 33D80, 20G41
Record Number:CaltechAUTHORS:20160425-090534476
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20160425-090534476
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:66440
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:03 May 2016 03:26
Last Modified:03 May 2016 03:26

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