Jones polynomials of torus knots via DAHA

Understand

We suggest a new construction for the Quantum Groups - Jones polynomials of torus knots in terms of the PBW theorem of DAHA for any root systems and weights (justified for type A).

• The main focus is on the DAHA super-polynomials, a stable 3-parametric type A variant of this construction.
• A connection is expected with the approach to super-polynomials due to Aganagic and Shakirov via the Macdonald polynomials at roots of unity and the Verlinde algebra.
• The duality conjecture for the DAHA super-polynomials is stated, essentially matching that due to Gukov and Stosic.