TY - JOUR
T1 - The Solution of the Quantum A 1 T-System for Arbitrary Boundary
AU - Di Francesco, Philippe
AU - Kedem, Rinat
PY - 2012/7
Y1 - 2012/7
N2 - We solve the quantum version of the A 1 T-system by use of quantum networks. The system is interpreted as a particular set of mutations of a suitable (infinite-rank) quantum cluster algebra, and Laurent positivity follows from our solution. As an application we re-derive the corresponding quantum network solution to the quantum A 1 Q-system and generalize it to the fully non-commutative case. We give the relation between the quantum T-system and the quantum lattice Liouville equation, which is the quantized Y-system.
AB - We solve the quantum version of the A 1 T-system by use of quantum networks. The system is interpreted as a particular set of mutations of a suitable (infinite-rank) quantum cluster algebra, and Laurent positivity follows from our solution. As an application we re-derive the corresponding quantum network solution to the quantum A 1 Q-system and generalize it to the fully non-commutative case. We give the relation between the quantum T-system and the quantum lattice Liouville equation, which is the quantized Y-system.
UR - http://www.scopus.com/inward/record.url?scp=84862886114&partnerID=8YFLogxK
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U2 - 10.1007/s00220-012-1488-x
DO - 10.1007/s00220-012-1488-x
M3 - Article
AN - SCOPUS:84862886114
VL - 313
SP - 329
EP - 350
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
SN - 0010-3616
IS - 2
ER -