Inhomogeneous spin $q$-Whittaker polynomials

TL;DR

This paper introduces inhomogeneous spin q-Whittaker polynomials, providing their fundamental properties, identities, and integral representations, using a new approach based on deformed Yang-Baxter equations.

Contribution

It presents the first inhomogeneous generalization of spin q-Whittaker polynomials with new identities and integral formulas, expanding the theoretical framework of symmetric polynomials.

Findings

Established branching rules and Cauchy identities

Derived integral representations for the polynomials

Developed a novel family of deformed Yang-Baxter equations

Abstract

We introduce and study an inhomogeneous generalization of the spin $q$-Whittaker polynomials from [Borodin,Wheeler-17]. These are symmetric polynomials, and we prove a branching rule, skew dual and non-dual Cauchy identities, and an integral representation for them. Our main tool is a novel family of deformed Yang-Baxter equations.