A Note on $$\mathfrak {gl}_{m|n}$$ Link Invariants and the HOMFLY–PT Polynomial

Queffelec, Hoel; Sartori, Antonio

doi:10.1007/978-3-030-16031-9_13

Cited by 2 publications

(3 citation statements)

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“…The same is true from the quantum supergroup point of view. In fact in [11] it has been proven, that U q (sl(N |M )) knot polynomials are equal to those of U q (sl(N − M ))…”

Section: The Knot Invariant For Su (N |M ) Is Equal (Possibly Up To F...mentioning

confidence: 99%

“…It generalizes the colored Jones, Alexander and the sl(N ) Reshetikhin-Turaev invariants. Their common property is that they arise from representations of sl(N |M ) superalgebras [10,11].…”

Section: Introductionmentioning

confidence: 99%

“…• It is a specific incarnation of the eigenvalue conjecture 3 Supergroup knot invariants Knot invariants originating from supergroups have been quite extensively studied . As usual they can be approached in two ways: studying supegroup Chern-Simons theory [23,24] or quantum invariants given by U q (sl(N |M )) [11,25]. Supergroup Chern-Simons theory was in described in detail in [23,24].…”

Section: Introductionmentioning

confidence: 99%

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A novel symmetry of colored HOMFLY polynomials coming from $\mathfrak{sl}(N|M)$ superalgebras

Mishnyakov,

Sleptsov,

Tselousov

2020

Preprint

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We present a novel symmetry of the colored HOMFLY polynomial. It relates pairs of polynomials colored by different representations at specific values of N and generalizes the previously known "tug-the-hook" symmetry of the colored Alexander polynomial [1]. As we show, the symmetry has a superalgebra origin, which we discuss qualitatively. Our main focus are the constraints that such a property imposes on the general group-theoretical structure, namely the sl(N ) weight system, arising in the perturbative expansion of the invariant. Finally, we demonstrate its tight relation to the eigenvalue conjecture.

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“…The same is true from the quantum supergroup point of view. In fact in [11] it has been proven, that U q (sl(N |M )) knot polynomials are equal to those of U q (sl(N − M ))…”

Section: The Knot Invariant For Su (N |M ) Is Equal (Possibly Up To F...mentioning

confidence: 99%

“…It generalizes the colored Jones, Alexander and the sl(N ) Reshetikhin-Turaev invariants. Their common property is that they arise from representations of sl(N |M ) superalgebras [10,11].…”

Section: Introductionmentioning

confidence: 99%