# Spin $q$-Whittaker polynomials

## TL;DR

This paper introduces a new family of symmetric polynomials called spin q-Whittaker polynomials, extending q-Whittaker functions with a fusion-based construction and establishing their fundamental algebraic identities.

## Contribution

It presents the first construction and analysis of spin q-Whittaker polynomials, including their branching, Pieri rules, and summation identities, expanding the theory of symmetric functions.

## Key findings

- Established branching and Pieri rules for the new polynomials.
- Derived standard and dual Cauchy identities.
- Provided an integral representation for the 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.