Positivity of the \(T\)-system cluster algebra

zbMath1229.13019arXiv0908.3122MaRDI QIDQ2380306

Rinat Kedem, Philippe Di Francesco

Publication date: 26 March 2010

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0908.3122

Mathematics Subject Classification ID

Applications of graph theory (05C90) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Applications of Lie algebras and superalgebras to integrable systems (17B80) Cluster algebras (13F60)

Related Items

\(\tau\)-functions, Birkhoff factorizations and difference equations ⋮ Coxeter's frieze patterns at the crossroads of algebra, geometry and combinatorics ⋮ Periodicity and integrability for the cube recurrence ⋮ \((q,t)\)-characters of Kirillov-Reshetikhin modules of type \(A_r\) as quantum cluster variables ⋮ Quivers with subadditive labelings: classification and integrability ⋮ Kirillov-Reshetikhin crystals \(B^{1, s}\) for \(\widehat{\mathfrak{s}\mathfrak{l}}_n\) using Nakajima monomials ⋮ Quantum unipotent subgroup and dual canonical basis ⋮ Non-commutative integrability, paths and quasi-determinants ⋮ The solution of the quantum \(A_1\) \(T\)-system for arbitrary boundary ⋮ \(Q\)-systems, heaps, paths and cluster positivity ⋮ 2-frieze patterns and the cluster structure of the space of polygons ⋮ \(SL_k\)-tilings of the plane ⋮ Hankel Determinant Solutions to Several Discrete Integrable Systems and the Laurent Property ⋮ Non-probabilistic fermionic limit shapes