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2012

Torus HOMFLY as the Hall-Littlewood Polynomials

Mironov, A., Morozov, A., Shakirov, Sh.

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We show that the HOMFLY polynomials for torus knots T[m,n] in all fundamental representations are equal to the Hall-Littlewood polynomials in representation which depends on m, and with quantum parameter, which depends on n.

This makes the long-anticipated interpretation of Wilson averages in 3d Chern-Simons theory as characters precise, at least for the torus knots, and calls for further studies in this direction.
This fact is deeply related to Hall-Littlewood-MacDonald duality of character expansion of superpolynomials found in arXiv:1201.3339.
In fact, the relation continues to hold for extended polynomials, but the symmetry between m and n is broken, then m is the number of strands in the braid.

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