A nonsymmetric version of okounkov’s bc-type interpolation macdonald polynomials

Nonsymmetric interpolation Laurent polynomials in n variables are introduced, with the interpolation points depending on q and on a n -tuple of parameters τ = ( τ 1 , …, τ n ). When τ i = st n − 1 , Okounkov’s 3-parameter BC n -type interpolation Macdonald polynomials are recovered from the nonsymmetric interpolation Laurent polynomials through Hecke algebra symmetrisation with respect to a type C n Hecke algebra action. In the Appendix we give some conjectures about extra vanishing, based on Mathematica computations in rank two.