---
abstract: 'In this paper, we recall our renormalized quantum Q-system associated with representations of the Lie algebra $A_r$, and show that it can be viewed as a quotient of the quantum current algebra $U_q(\n[u,u^{-1}])\subset U_q(\widehat{\sl}_2)$ in the Drinfeld presentation. Moreover, we find the interpretation of the conserved quantities in terms of Cartan currents at level 0, and the rest of the current algebra, in a non-standard polarization in terms of generators in the quantum cluster algebra.'
address:
- 'PDF: Department of Mathematics, University of Illinois MC-382, Urbana, IL 61821, U.S.A. e-mail: philippe@illinois.edu'
- 'RK: Department of Mathematics, University of Illinois MC-382, Urbana, IL 61821, U.S.A. e-mail: rinat@illinois.edu'
author:
- Philippe Di Francesco
- Rinat Kedem
bibliography:
- 'refs.bib'
title: 'Quantum Q systems: From cluster algebras to quantum current algebras'
---

Introduction
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An extended quantum Q system
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Proofs {#proofsec}
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The quantum affine algebra
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Discussion/Conclusion
=====================
