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 $\tau =({\tau }_1,\dots ,{\tau }_n)$. When ${\tau }_i=s{t}^{n-i}$ Okounkov’s $3$-parameter $B{C}_n$-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.