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International Conference on KNOTS

KNOTS16 2016: Knots, Low-Dimensional Topology and Applications pp 277–286Cite as

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

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 284))

Abstract

We present a short and unified representation-theoretical treatment of type A link invariants (that is, the HOMFLY–PT polynomials, the Jones polynomial, the Alexander polynomial and, more generally, the quantum \(\mathfrak {gl}_{m|n}\) invariants) as link invariants with values in the quantized oriented Brauer category.

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Notes

  1. 1.

    Note that to precisely match the definitions, one should replace q by \(q^{-1}\) and \(q^{\beta }\) by \(q^{-\beta }\).

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Acknowledgements

H.Q. was funded by the ARC DP 140103821.

Author information

Authors and Affiliations

  1. IMAG, Univ Montpellier, CNRS, Montpellier, France

    Hoel Queffelec

  2. Mathematisches Institut, Albert-Ludwigs-Universität Freiburg, Eckerstrasse 1, 79104, Freiburg in Breisgau, Germany

    Antonio Sartori

Authors
  1. Hoel Queffelec
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  2. Antonio Sartori
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Corresponding author

Correspondence to Hoel Queffelec .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Williams College, Williamstown, MA, USA

    Colin C. Adams

  2. Department of Mathematics, University of Texas at Austin, Austin, TX, USA

    Cameron McA. Gordon

  3. Department of Mathematics, Vanderbilt University, Nashville, TN, USA

    Vaughan F.R. Jones

  4. Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL, USA

    Louis H. Kauffman

  5. School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Athens, Greece

    Sofia Lambropoulou

  6. Department of Mathematics, University of California, Santa Barbara, Santa Barbara, CA, USA

    Kenneth C. Millett

  7. Department of Mathematics, Columbian College of Arts & Sciences, George Washington University, Washington, DC, USA

    Jozef H. Przytycki

  8. Department of Mathematics and Applications, University of Milano-Bicocca, Milano, Italy

    Renzo Ricca

  9. Department of Mathematics, North Carolina State University, Raleigh, NC, USA

    Radmila Sazdanovic

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Queffelec, H., Sartori, A. (2019). A Note on \(\mathfrak {gl}_{m|n}\) Link Invariants and the HOMFLY–PT Polynomial. In: Adams, C., et al. Knots, Low-Dimensional Topology and Applications. KNOTS16 2016. Springer Proceedings in Mathematics & Statistics, vol 284. Springer, Cham. https://doi.org/10.1007/978-3-030-16031-9_13

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