Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: DAHA-Jones polynomials of torus knots   DAHA-Jones polynomials of torus knots $T(r,s)$ are studied systematically for
reduced root systems and in the case of $C^\vee C_1$. We prove the
polynomiality and evaluation conjectures from the author's previous paper on
torus knots and extend the theory by the color exchange and further symmetries.
DAHA-Jones polynomials for $C^\vee C_1$ depend on $5$ parameters. Their
surprising connection to the DAHA-superpolynomials (type $A$) for the knots
$T(2p+1,2)$ is obtained, a remarkable combination of the color exchange
conditions and the author's duality conjecture (justified by Gorsky and Negut).
The DAHA-superpolynomials for symmetric and wedge powers (and torus knots)
conjecturally coincide with the Khovanov-Rozansky stable polynomials, those
originated in the theory of BPS states and the superpolynomials defined via
rational DAHA in connection with certain Hilbert schemes, though not much is
known about such connections beyond the HOMFLYPT and Kauffman polynomials. We
also define certain arithmetic counterparts of DAHA-Jones polynomials for the
absolute Galois group instead of torus knots in the case of $C^\vee C_1$.

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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc