  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. A link to Khovanov-Rozansky
polynomials is provided, including small N (for some torus knots). The
hyper-polynomials of types B and C are defined, generalizing the Kauffman
invariants and containing an extra parameter vs. the super-polynomials. The
special values and other features of the DAHA super and hyper-polynomials are
discussed; there are many examples in the paper.
