Representation theoretic interpretation and interpolation properties of inhomogeneous spin q-Whittaker polynomials

We establish new properties of inhomogeneous spin q -Whittaker polynomials, which are symmetric polynomials generalizing $$t=0$$ t = 0 Macdonald polynomials. We show that these polynomials are defined in terms of a vertex model, whose weights come not from an R -matrix, as is often the case, but from other intertwining operators of U'q(sl₂) U q ′ ( sl ^ 2 ) -modules. Using this construction, we are able to prove a Cauchy-type identity for inhomogeneous spin q -Whittaker polynomials in full generality. Moreover, we are able to characterize spin q -Whittaker polynomials in terms of vanishing at certain points, and we find interpolation analogues of q -Whittaker and elementary symmetric polynomials.