The Solution of the Quantum A 1 T-System for Arbitrary Boundary
| Autor: | Philippe Di Francesco, Rinat Kedem |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
Complex system
FOS: Physical sciences Boundary (topology) 01 natural sciences Cluster algebra Set (abstract data type) Lattice (order) Mathematics - Quantum Algebra 0103 physical sciences FOS: Mathematics Mathematics - Combinatorics Quantum Algebra (math.QA) Representation Theory (math.RT) 0101 mathematics Quantum Mathematical Physics Mathematical physics Physics Quantum network Liouville equation 010102 general mathematics Statistical and Nonlinear Physics Mathematical Physics (math-ph) Combinatorics (math.CO) 010307 mathematical physics Mathematics - Representation Theory |
| Zdroj: | Communications in Mathematical Physics. 313:329-350 |
| ISSN: | 1432-0916 0010-3616 |
| DOI: | 10.1007/s00220-012-1488-x |
| Popis: | 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. Comment: 24 pages, 18 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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