Periodicities of T-systems and Y-systems, dilogarithm identities, and cluster algebras. II: Types \(C_r, F_4\), and \(G_2\)

DOI10.4171/PRIMS/96zbMath1283.13021arXiv1001.1881OpenAlexW1519423474MaRDI QIDQ1946987

Osamu Iyama, Tomoki Nakanishi, Rei Inoue, Keller, Bernhard, Atsuo Kuniba

Publication date: 11 April 2013

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.1881

zbMATH Keywords

dilogarithmcluster algebraT-systemsY-systems

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Cluster algebras (13F60)

Related Items (19)

Équations fonctionnelles du dilogarithme ⋮ Positivity and periodicity of \(Q\)-systems in the WZW fusion ring ⋮ Exponents associated with \(Y\)-systems and their relationship with \(q\)-series ⋮ Quivers with subadditive labelings: classification and integrability ⋮ Cluster algebra structures on module categories over quantum affine algebras ⋮ The periodicity conjecture for pairs of Dynkin diagrams ⋮ Monoidal categorification and quantum affine algebras. II ⋮ Periodicities of T-systems and Y-systems, dilogarithm identities, and cluster algebras. I: Type \(B_r\) ⋮ Quantum trilogy: discrete Toda, Y-system and chaos ⋮ Rogers-Ramanujan type identities and nil-DAHA ⋮ \(T\)-systems and the pentagram map ⋮ Periodicity, linearizability, and integrability in seed mutations of type AN(1) ⋮ Relation between \(f\)-vectors and \(d\)-vectors in cluster algebras of finite type or rank 2 ⋮ Wall-crossing, Rogers dilogarithm, and the QK/HK correspondence ⋮ On the extended T-system of type \(C_3\) ⋮ MHV amplitudes at strong coupling and linearized TBA equations ⋮ Wonder of sine-Gordon $Y$-systems ⋮ Difference equations arising from cluster algebras ⋮ Generators of rank 2 cluster algebras of affine types via linearization of seed mutations

Cites Work

• Cluster characters for cluster categories with infinite-dimensional morphism spaces
• \(Y\)-systems and generalized associahedra
• Identities for the Rogers dilogarithm function connected with simple Lie algebras
• Periodicities of T-systems and Y-systems, dilogarithm identities, and cluster algebras. I: Type \(B_r\)
• SPECTRA IN CONFORMAL FIELD THEORIES FROM THE ROGERS DILOGARITHM
• FUNCTIONAL RELATIONS IN SOLVABLE LATTICE MODELS I: FUNCTIONAL RELATIONS AND REPRESENTATION THEORY
• Cluster algebras, quiver representations and triangulated categories
• Cluster algebras via cluster categories with infinite-dimensional morphism spaces
• Cluster algebras IV: Coefficients
• Periodicities of T-systems and Y-systems

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