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

Research output: Contribution to journalArticle

Abstract

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
Volume313
Issue number2
DOIs
StatePublished - Jul 1 2012

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Liouville equations
Arbitrary
mutations
algebra
Cluster Algebra
Liouville Equation
Quantum Algebra
Positivity
Mutation
Generalise

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

The Solution of the Quantum A 1 T-System for Arbitrary Boundary. / Di Francesco, Philippe; Kedem, Rinat.

In: Communications in Mathematical Physics, Vol. 313, No. 2, 01.07.2012, p. 329-350.

Research output: Contribution to journalArticle

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