Periodicities of T-systems and Y-systems, dilogarithm identities, and cluster algebras. I: Type \(B_r\)
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Publication:1946986
DOI10.4171/PRIMS/95zbMath1273.13041arXiv1001.1880OpenAlexW2110492153MaRDI QIDQ1946986
Tomoki Nakanishi, Osamu Iyama, 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/1001.1880
Quantum groups (quantized enveloping algebras) and related deformations (17B37) Cluster algebras (13F60)
Related Items (27)
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 ⋮ Plabic R-matrices ⋮ 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 ⋮ A CONJECTURE ON -MATRICES OF CLUSTER ALGEBRAS ⋮ Monoidal categorification and quantum affine algebras. II ⋮ Periodicities of T-systems and Y-systems, dilogarithm identities, and cluster algebras. II: Types \(C_r, F_4\), and \(G_2\) ⋮ Quantum trilogy: discrete Toda, Y-system and chaos ⋮ Rogers dilogarithms of higher degree and generalized cluster algebras ⋮ Cluster realization of Weyl groups and \(q\)-characters of quantum affine algebras ⋮ On the cluster nature and quantization of geometric \(R\)-matrices ⋮ 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 ⋮ Dilogarithm identities for conformal field theories and cluster algebras: Simply laced case ⋮ 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 ⋮ Cluster realizations of Weyl groups and higher Teichmüller theory ⋮ Difference equations arising from cluster algebras ⋮ Existence and uniqueness of solutions to \(Y\)-systems and TBA equations ⋮ Generators of rank 2 cluster algebras of affine types via linearization of seed mutations ⋮ Synchronicity phenomenon in cluster patterns ⋮ Cluster algebras: an introduction
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