Quadratic Harnesses, q-commutations, and orthogonal martingale   polynomials
  We introduce the quadratic harness condition and show that integrable quadratic harnesses have orthogonal martingale polynomials with a three step recurrence that satisfies a q-commutation relation. This implies that quadratic harnesses are essentially determined uniquely by five numerical constants. Explicit recurrences for the orthogonal martingale polynomials are derived in several cases of interest. 
Wlodzimierz Bryc, Wojciech Matysiak, Jacek Wesolowski