Quantum $A_r$ Q-system solutions as q-multinomial series

TL;DR

This paper derives explicit generating series solutions for the quantum $A_r$ $Q$-system, expressed through quantum multinomial coefficients based on initial data, advancing the understanding of quantum integrable systems.

Contribution

It provides explicit formulas for the solutions of the quantum $A_r$ $Q$-system using quantum multinomial coefficients, generalizing previous implicit descriptions.

Findings

Explicit generating series formulas derived

Solutions expressed in terms of quantum multinomial coefficients

Applicable to any admissible initial data

Abstract

We derive explicit expressions for the generating series of the fundamental solutions of the $A_r$ quantum $Q$-system of Ref. [P. Di Francesco and R. Kedem, arXiv:1006.4774 [math-ph]], expressed in terms of any admissible initial data. These involve products of quantum multinomial coefficients, coded by the initial data structure.