Title: Spin $q$-Whittaker polynomials,
Abstract: We introduce and study a one-parameter generalization of the q-Whittaker
symmetric functions. This is a family of multivariate symmetric polynomials,
whose construction may be viewed as an application of the procedure of fusion
from integrable lattice models to a vertex model interpretation of a
one-parameter generalization of Hall-Littlewood polynomials from [Bor17, BP16a,
BP16b].
We prove branching and Pieri rules, standard and dual (skew) Cauchy summation
identities, and an integral representation for the new polynomials.