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- W2788532020 abstract "A bstract R -coloured knot polynomials for m -strand torus knots Torus [ m , n ] are described by the Rosso-Jones formula, which is an example of evolution in n with Lyapunov exponents, labelled by Young diagrams from R ⊗ m . This means that they satisfy a finite-difference equation (recursion) of finite degree. For the gauge group SL( N ) only diagrams with no more than N lines can contribute and the recursion degree is reduced. We claim that these properties (evolution/recursion and reduction) persist for Khovanov-Rozansky (KR) polynomials, obtained by additional factorization modulo 1 + t , which is not yet adequately described in quantum field theory. Also preserved is some weakened version of differential expansion, which is responsible at least for a simple relation between reduced and unreduced Khovanov polynomials. However, in the KR case evolution is incompatible with the mirror symmetry under the change n −→ − n , what can signal about an ambiguity in the KR factorization even for torus knots." @default.
- W2788532020 created "2018-03-06" @default.
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- W2788532020 date "2018-04-01" @default.
- W2788532020 modified "2023-09-23" @default.
- W2788532020 title "Are Khovanov-Rozansky polynomials consistent with evolution in the space of knots?" @default.
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- W2788532020 doi "https://doi.org/10.1007/jhep04(2018)066" @default.
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