Elliot, Ross and Gukov, Sergei (2016) Exceptional knot homology. Journal of Knot Theory and its Ramifications, 25 (3). Art. No. 1640003. ISSN 0218-2165. doi:10.1142/S0218216516400034. https://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.
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| 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 | ||||||||||||
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| Subject Keywords: | BPS states; double affine Hecke algebras; superpolynomials; knot homology; quantum invariants; exceptional Lie algebras; singularity theory; Landau–Ginzburg potential | ||||||||||||
| Issue or Number: | 3 | ||||||||||||
| Classification Code: | AMSC: 57M27, 81T30, 33D80, 20G41 | ||||||||||||
| DOI: | 10.1142/S0218216516400034 | ||||||||||||
| Record Number: | CaltechAUTHORS:20160425-090534476 | ||||||||||||
| Persistent URL: | https://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: | 10 Nov 2021 23:58 |
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