A Novel Symmetry of Colored HOMFLY Polynomials Coming from $$\mathfrak {sl}(N|M)$$ Superalgebras

Mishnyakov, Victor; Слепцов, А.; Tselousov, N.

doi:10.1007/s00220-021-04073-3

Cited by 13 publications

(9 citation statements)

References 39 publications

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“…where T N is a transformation of Young diagrams which pulls the diagram inside the (N + M |M ) fat hook. We provide an example of the tug-the-hook transformations with N = 2, M = 2 : This symmetry has the supergroup origin [28]. The Reshetikhin-Turaev quantum knot invariants for quantum superqroup U q (sl(N |M ) and quantum group U q (sl(|N − M |) exactly coincide.…”

Section: Symmetries Of the Colored Homfly Polynomialsmentioning

confidence: 94%

“…At the end of the section we argue that the tug-the-hook symmetry does not restricts the form of the group factors. The tug-the-hook symmetry [28] of the colored HOMFLY polynomials reads:…”

Section: Symmetries Of the Colored Homfly Polynomialsmentioning

confidence: 99%

“…The complexity restricts the number of available answers, which makes the bigger picture/internal structure of the colored HOMFLY polynomials concealed for the present moment. Recent studies of the colored HOMFLY polynomials and the discovery of new symmetries and related structures [25][26][27][28] motivate us to return to the question about the perturbative expansion of the Chern-Simons correlators:…”

Section: Introductionmentioning

confidence: 99%

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Chern-Simons perturbative series revisited

Lanina,

Sleptsov,

Tselousov

2021

Preprint

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A group-theoretical structure in the perturbative expansion for the Wilson loops in the 3d Chern-Simons theory with SU (N ) gauge group is developed in symmetric approach. An image of a map called slN weight system from the algebra of chord diagrams to the center of the universal enveloping algebra ZU (slN ) is studied. Elements of the image -group factors, were known only up to the 6-th order in some representations. We present the group factors in arbitrary representation up to the 9-th order. Developed methods have wide applications, we mention straightforward and evident examples. In particular, these methods allow us to compute the Vassiliev invariants of higher orders and also prove the existence of the recently discovered tug-the-hook symmetry of the colored HOMFLY polynomial.

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Section: Symmetries Of the Colored Homfly Polynomialsmentioning

confidence: 94%

“…At the end of the section we argue that the tug-the-hook symmetry does not restricts the form of the group factors. The tug-the-hook symmetry [28] of the colored HOMFLY polynomials reads:…”

Section: Symmetries Of the Colored Homfly Polynomialsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Chern-Simons perturbative series revisited

Lanina,

Sleptsov,

Tselousov

2021

Preprint

Self Cite

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“…We present these expressions for the sake of reference. Namely, one can verify that (15,16) are reduced to (11), and the polynomials (19) explicitly given in sec.4.3,4.4 are reduced to (12) for t = −1.…”

Section: Summary Of Jones Formulaementioning

confidence: 97%

“…Another part of the story is the knot Floer homology, which is believed to be an other ("dual" to Khovanov) "reduction" of the superpolynomial [18,19]. The Floer homologies were studied both for the Whitehead doubles [20] and cables [21,22].…”

Section: Introductionmentioning

confidence: 99%

Khovanov polynomials for satellites and asymptotic adjoint polynomials

Anokhina,

Morozov,

Popolitov

2021

Preprint

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We compute explicitly the Khovanov polynomials (using the computer program from katlas.org) for the two simplest families of the satellite knots, which are the twisted Whitehead doubles and the twostrand cables. We find that a quantum group decomposition for the HOMFLY polynomial of a satellite knot can be extended to the Khovanov polynomial, whose quantum group properties are not manifest. Namely, the Khovanov polynomial of a twisted Whitehead double or two-strand cable (the two simplest satellite families) can be presented as a naively deformed linear combination of the pattern and companion invariants. For a given companion, the satellite polynomial "smoothly" depends on the pattern but for the "jump" at one critical point defined by the s-invariant of the companion knot. A similar phenomenon is known for the knot Floer homology and τ -invariant for the same kind of satellites

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Spectral curves and W-representations of matrix models

Mironov

Морозов

2023

J. High Energ. Phys.

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We explain how the spectral curve can be extracted from the $$ \mathcal{W} $$ W -representation of a matrix model. It emerges from the part of the $$ \mathcal{W} $$ W -operator, which is linear in time-variables. A possibility of extracting the spectral curve in this way is important because there are models where matrix integrals are not yet available, and still they possess all their important features. We apply this reasoning to the family of WLZZ models and discuss additional peculiarities which appear for the non-negative value of the family parameter n, when the model depends on additional couplings (dual times). In this case, the relation between topological and 1/N expansions is broken. On the other hand, all the WLZZ partition functions are τ-functions of the Toda lattice hierarchy, and these models also celebrate the superintegrability properties.

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A Novel Symmetry of Colored HOMFLY Polynomials Coming from $$\mathfrak {sl}(N|M)$$ Superalgebras

Cited by 13 publications

References 39 publications

Chern-Simons perturbative series revisited

Chern-Simons perturbative series revisited

Khovanov polynomials for satellites and asymptotic adjoint polynomials

Spectral curves and W-representations of matrix models

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