TY - JOUR

T1 - The Solution of the Quantum A 1 T-System for Arbitrary Boundary

AU - Di Francesco, Philippe

AU - Kedem, Rinat

N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.

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 -