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

Philippe Di Francesco; Rinat Kedem

doi:10.1007/s00220-012-1488-x

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

Philippe Di Francesco, Rinat Kedem

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	329-350
Number of pages	22
Journal	Communications in Mathematical Physics
Volume	313
Issue number	2
DOIs	https://doi.org/10.1007/s00220-012-1488-x
State	Published - Jul 2012

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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