We consider a fully inhomogeneous stochastic higher spin six vertex model ina quadrant. For this model we derive concise integral representations formulti-point q-moments of the height function and for the q-correlationfunctions. At least in the case of the step initial condition, our formulasdegenerate in appropriate limits to many known formulas of such type forintegrable probabilistic systems in the (1+1)d KPZ universality class,including the stochastic six vertex model, ASEP, various q-TASEPs, andassociated zero range processes. Our arguments are largely based on properties of a family of symmetricrational functions which can be defined as partition functions of theinhomogeneous higher spin six vertex model for suitable domains. In thehomogeneous case, such functions were previously studied inhttp://arxiv.org/abs/1410.0976; they also generalize classical Hall-Littlewoodand Schur polynomials. A key role is played by Cauchy-like summation identitiesfor these functions, which are obtained as a direct corollary of theYang-Baxter equation for the higher spin six vertex model.
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