Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The SL_3 colored Jones polynomial of the trefoil   Rosso and Jones gave a formula for the colored Jones polynomial of a torus
knot, colored by an irreducible representation of a simple Lie algebra. The
Rosso-Jones formula involves a plethysm function, unknown in general. We
provide 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,n) torus
knots. We give two independent proofs of our plethysm formula, one of which
uses the work of Carini-Remmel. Our formula for the $\fsl_3$ colored Jones
polynomial of T(2,n) torus knots allows us to verify the Degree Conjecture for
those knots, to efficiently the $\fsl_3$ Witten-Reshetikhin-Turaev invariants
of the Poincare sphere, and to guess a Groebner basis for recursion ideal of
the $\fsl_3$ colored Jones polynomial of the trefoil.

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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex