Implications for colored HOMFLY polynomials from explicit formulas for group-theoretical structure

Lanina, E.; Слепцов, А.; Tselousov, N.

doi:10.1016/j.nuclphysb.2021.115644

Cited by 5 publications

(1 citation statement)

References 58 publications

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“…which depend on integration contour (knot) K, the coupling constant g, the size N of the sl N gauge algebra and its representation R. Dependence on g and N is actually through the non-perturbative variables q = exp 2πi g+N and A = q N , of which H K is -mysteriously -just a polynomial. For a recent progress in perturbative approach see [51,52]. Dependence on K and R is more tricky, and the better (less redundant) variables are the coefficients F K Q of the differential (cyclotomic) expansion , which we write down restricted in two ways -to symmetric representations and to defect [23] zero -according to the limited consideration in this paper.…”

Section: Differential Expansion (De)mentioning

confidence: 99%

Differential Expansion for antiparallel triple pretzels: the way the factorization is deformed

Morozov¹,

Tselousov²

2022

Preprint

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For a peculiar family of double braid knots there is a remarkable factorization formula for the coefficients of the differential (cyclotomic) expansion (DE), which nowadays is widely used to construct the exclusive Racah matrices S and S in arbitrary representations. The origins of the factorization remain obscure and the special role of double braids remains a mystery. In an attempt to broaden the perspective, we extend the family of double braids to antiparallel triple pretzels, which are obtained by the defect-preserving deformation from the trefoil and all have defect zero. It turns out that factorization of DE coefficients is violated quite strongly, still remains described by an elegant formula, at least for all symmetric representations.

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Section: Differential Expansion (De)mentioning

confidence: 99%

Differential Expansion for antiparallel triple pretzels: the way the factorization is deformed

Morozov¹,

Tselousov²

2022

Preprint

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Machine learning of the well-known things

2023

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Evolution properties of the knot’s defect

Морозов

Tselousov

2022

Eur. Phys. J. C

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The defect of differential (cyclotomic) expansion for colored HOMFLY-PT polynomials is conjectured to be invariant under any antiparallel evolution and change linearly with the evolution in any parallel direction. In other words, each $${{\mathcal {R}}}$$ R -matrix can be substituted by an entire 2-strand braid in two different ways: the defect remains intact when the braid is antiparallel and changes by half of the added length when the braid is parallel.

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Implications for colored HOMFLY polynomials from explicit formulas for group-theoretical structure

Cited by 5 publications

References 58 publications

Differential Expansion for antiparallel triple pretzels: the way the factorization is deformed

Differential Expansion for antiparallel triple pretzels: the way the factorization is deformed

Machine learning of the well-known things

Evolution properties of the knot’s defect

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