Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 3, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP03(2012)034
Keywords
Quantum Groups; Chern-Simons Theories; Topological Field Theories
Categories
Funding
- Ministry of Education and Science of the Russian Federation [14.740.11.081]
- RFBR [10-02-00509, 10-02-00499, 10-02-01315]
- [11-02-90453-Ukr]
- [09-02-93105-CNRSL]
- [09-02-91005-ANF]
- [10-02-92109-Yaf-a]
- [11-01-92612-Royal Society]
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Character expansion is introduced and explicitly constructed for the (non-colored) HOMFLY polynomials of the simplest knots. Expansion coefficients are not the knot invariants and can depend on the choice of the braid realization. However, the method provides the simplest systematic way to construct HOMFLY polynomials directly in terms of the variable A = q(N) : a much better way than the standard approach making use of the skein relations. Moreover, representation theory of the simplest quantum group SUq (2) is sufficient to get the answers for all braids with m < 5 strands. Most important we reveal a hidden hierarchical structure of expansion coefficients, what allows one to express all of them through extremely simple elementary constituents. Generalizations to arbitrary knots and arbitrary representations is straightforward.
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