Thao Vuong

  1. The SL_3 colored Jones polynomial of the trefoil.

    Authors: Stavros Garoufalidis, Thao Vuong
    Subjects: Geometric Topology
    Abstract

    Jones and Rosso gave a formula for the colored Jones polynomial of a torus
    knot, colored by an irreducible representation of a simple Lie algebra. The
    Jones-Rosso formula involves a plethysm function, unknown in general. Our main
    result is an explicit formula for the second plethysm of an arbitrary
    representation of $\fsl_3$, which allows us to give an explicit formula for the
    colored Jones polynomial of the trefoil (and more generally, for $T(2,b)$ torus
    knots). Our formula is different from the one given by R.

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