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- W4300339717 abstract "From analysis of a big variety of different knots we conclude that at q which is an root of unity, q^{2m}=1, HOMFLY polynomials in symmetric representations [r] satisfy recursion identity: H_{r+m} = H_r H_m for any A, which is a generalization of the property H_r = (H_1)^r for special polynomials at q=1. We conjecture a natural generalization to arbitrary representation R, which, however, is checked only for torus knots. Next, Kashaev polynomial, which arises from H_R at q=exp(ipi/|R|), turns equal to the special polynomial with A substituted by A^|R|, provided R is a single-hook representations (e.g. arbitrary symmetric) -- what provides a q-A dual to the similar property of Alexander polynomial. All this implies non-trivial relations for the coefficients of the differential expansions, which are believed to provide reasonable coordinates in the space of knots -- existence of such universal relations means that these variables are still not unconstrained." @default.
- W4300339717 created "2022-10-03" @default.
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- W4300339717 creator A5020381407 @default.
- W4300339717 date "2015-05-22" @default.
- W4300339717 modified "2023-09-25" @default.
- W4300339717 title "Factorization of colored knot polynomials at roots of unity" @default.
- W4300339717 doi "https://doi.org/10.48550/arxiv.1505.06170" @default.
- W4300339717 hasPublicationYear "2015" @default.
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