# 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 $U_q({\mathfrak n}[u,u^{-1}])\subset U_q(\widehat{\mathfrak sl}_2)$ 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.
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https://hal-cea.archives-ouvertes.fr/cea-01531365
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### Citation

Philippe Di Francesco, Rinat Kedem. Quantum Q systems: from cluster algebras to quantum current algebras. Letters in Mathematical Physics, Springer Verlag, 2016, 107, pp.301 - 341. ⟨10.1007/s11005-016-0902-2⟩. ⟨cea-01531365⟩

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