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

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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.

Original languageEnglish (US)
Pages (from-to)329-350
Number of pages22
JournalCommunications in Mathematical Physics
Issue number2
StatePublished - Jul 2012

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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