In attempt to prove (and compute) a formula for the dimensions of the HOMFLY homology of the (p,q)-torus knot one could try to follow original proof by Jones of a formula for HOMFLY polynomial of the torus knot. One of the key moments of the Jones proof is Schur-Weyl duality and Schur's Lemma. Then the question:

What is a categorical analogues of the Schur's Lemma and Schur-Weyl duality. In general what are the obstacles for finding formula for the HOMLFLY homology of the (p,q)-torus knot. Any refs and suggestions would be greatly appreciated.