q-holonomic formulas for colored HOMFLY polynomials of 2-bridge links

@article{Wedrich2019qholonomicFF,
  title={q-holonomic formulas for colored HOMFLY polynomials of 2-bridge links},
  author={Paul Wedrich},
  journal={Journal of Pure and Applied Algebra},
  year={2019}
}
  • Paul Wedrich
  • Published 14 October 2014
  • Mathematics
  • Journal of Pure and Applied Algebra
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References

SHOWING 1-10 OF 15 REFERENCES
THE COLORED HOMFLY POLYNOMIAL IS q-HOLONOMIC
We prove that the colored HOMFLY polynomial of a link, colored by symmetric or exterior powers of the fundamental representation, is q-holonomic with respect to the color parameters. As a result, we
The colored HOMFLYPT function is $q$-holonomic
We prove that the HOMFLYPT polynomial of a link, colored by partitions with a xed number of rows is a q-holonomic function. Specializing to the case of knots colored by a partition with a single row,
Categorified N invariants of colored rational tangles
We use categorical skew Howe duality to find recursion rules that compute categorified slN invariants of rational tangles colored by exterior powers of the standard representation. Further, we offer
The colored Jones function is q-holonomic
A function of several variables is called holonomic if, roughly speaking, it is determined from finitely many of its values via finitely many linear recursion relations with polynomial coefficients.
Super $q$-Howe duality and web categories
We use super $q$-Howe duality to provide diagrammatic presentations of an idempotented form of the Hecke algebra and of categories of $\mathfrak{gl}_N$-modules (and, more generally,
On a proof of the Labastida-Marino-Ooguri-Vafa conjecture
We outline a proof of a remarkable conjecture of Labastida-Mari{\~n}o-Ooguri-Vafa about certain new algebraic structures of quantum link invariants and the integrality of infinite family of new
Homological algebra of knots and BPS states
It is known that knot homologies admit a physical description as spaces of open BPS states. We study operators and algebras acting on these spaces. This leads to a very rich story, which involves
An algorithmic proof theory for hypergeometric (ordinary and “q”) multisum/integral identities
SummaryIt is shown that every ‘proper-hypergeometric’ multisum/integral identity, orq-identity, with a fixed number of summations and/or integration signs, possesses a short, computer-constructible
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