DAHA-Jones polynomials of torus knots
type: Item
instance of: scholarly article
title: DAHA-Jones polynomials of torus knots
zbMATH Open document ID: 1360.14076
published in: Selecta Mathematica. New Series
publication date: 2016-04-14T00:00:00Z
full work available at URL: https://arxiv.org/abs/1406.3959
review text: The paper under review studies DAHA-Jones polynomials of torus knots for reduces root systems and in the case of \(C^\vee C_1\). The main results of the paper establish the polynomiality conjecture and the evaluation conjecture from a previous work by the author and extend the theory by studying the color exchange symmetry. The DAHA-Jones polynomials in the case \(C^\vee C_1\) are related to DAHA superpolynomials of type \(A\). A connection of DAHA superpolynomials to Kohavonov-Rozansky homology and superpolynomials defined via rational DAHA is discussed. Also, a connection to the absolute Galois group is investigated.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 14G32
Mathematics Subject Classification ID: 17B22
Mathematics Subject Classification ID: 17B45
Mathematics Subject Classification ID: 20C08
Mathematics Subject Classification ID: 20F36
Mathematics Subject Classification ID: 33D52
Mathematics Subject Classification ID: 30F10
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57R58
zbMATH DE Number: 6568893
zbMATH Keywords: double affine Hecke algebras
zbMATH Keywords: Jones polynomial
zbMATH Keywords: Khovanov-Rozansky homology
zbMATH Keywords: torus knot
zbMATH Keywords: Macdonald polynomial
zbMATH Keywords: Askey-Wilson polynomial
zbMATH Keywords: Verlinde algebra
zbMATH Keywords: Galois group
zbMATH Keywords: Chern-Simons theory
author: Ivan Cherednik
MaRDI profile type: Publication
OpenAlex ID: W2135832811
arXiv ID: 1406.3959
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DOI: 10.1007/S00029-015-0210-1
description: scientific article; zbMATH DE number 6568893