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Title: Colored knot polynomials for arbitrary pretzel knots and links

A very simple expression is conjectured for arbitrary colored Jones and HOMFLY polynomials of a rich (g+1)-parametric family of pretzel knots and links. The answer for the Jones and HOMFLY is fully and explicitly expressed through the Racah matrix of Uq(SUN), and looks related to a modular transformation of toric conformal block. Knot polynomials are among the hottest topics in modern theory. They are supposed to summarize nicely representation theory of quantum algebras and modular properties of conformal blocks. The result reported in the present letter, provides a spectacular illustration and support to this general expectation.
Authors:
 [1] ;  [2] ;  [3] ;  [4] ;  [5]
  1. ITEP, Moscow (Russia); Rutgers Univ., Piscataway, NJ (United States)
  2. ITEP, Moscow (Russia); International Institute of Physics, Natal (Brazil)
  3. Lebedev Physics Institute, Moscow (Russia); ITEP, Moscow (Russia); National Research Nuclear Univ., Moscow (Russia)
  4. ITEP, Moscow (Russia); National Research Nuclear Univ., Moscow (Russia)
  5. ITEP, Moscow (Russia); National Research Nuclear Univ., Moscow (Russia); Chelyabinsk State Univ., Chelyabinsk (Russia)
Publication Date:
OSTI Identifier:
1198587
Grant/Contract Number:
SC0010008; ARRA-SC0003883; SC0007897
Type:
Published Article
Journal Name:
Physics Letters. Section B
Additional Journal Information:
Journal Volume: 743; Journal Issue: C; Journal ID: ISSN 0370-2693
Publisher:
Elsevier
Research Org:
Rutgers Univ., Piscataway, NJ (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING