%0 Journal Article %T Quantum Q systems: from cluster algebras to quantum current algebras %+ Department of Mathematics, Illinois State University %+ Institut de Physique Théorique - UMR CNRS 3681 (IPHT) %A Di Francesco, Philippe %A Kedem, Rinat %Z 38 pages, 2 figures %< avec comité de lecture %@ 0377-9017 %J Letters in Mathematical Physics %I Springer Verlag %V 107 %P 301 - 341 %8 2016-06-29 %D 2016 %Z 1606.09052 %R 10.1007/s11005-016-0902-2 %Z Mathematics [math]/Quantum Algebra [math.QA] %Z Physics [physics]/Mathematical Physics [math-ph] %Z Mathematics [math]/Combinatorics [math.CO] %Z Mathematics [math]/Representation Theory [math.RT]Journal articles %X 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. %G English %2 https://cea.hal.science/cea-01531365/document %2 https://cea.hal.science/cea-01531365/file/1606.09052.pdf %L cea-01531365 %U https://cea.hal.science/cea-01531365 %~ CEA %~ CNRS %~ INSMI %~ DSM-IPHT %~ CEA-UPSAY %~ TDS-MACS %~ UNIV-PARIS-SACLAY %~ CEA-UPSAY-SACLAY %~ CEA-DRF %~ GS-MATHEMATIQUES %~ GS-PHYSIQUE