Quantum Q systems: From cluster algebras to quantum current algebras

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 $U_q(\mathfrak{n}[u,u^{-1}])\subset U_q({\widehat{\mathfrak{s}l}}_2)$ 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.

38 pages, 2 figures

References in corpus (2)

• Q-systems as cluster algebras
• Noncommutative integrability, paths and quasi-determinants