Periodicities of T-systems and Y-systems

DOI10.1215/00277630-2009-003zbMath1250.17024arXiv0812.0667OpenAlexW1579188450MaRDI QIDQ3558739

Atsuo Kuniba, Junji Suzuki, Osamu Iyama, Rei Inoue, Tomoki Nakanishi

Publication date: 6 May 2010

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0812.0667

zbMATH Keywords

Q-systemsT-systemsY-systemsperiodicity conjecture for the restricted \(Y\)-systems

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Exactly solvable models; Bethe ansatz (82B23) Groups and algebras in quantum theory and relations with integrable systems (81R12) Ring-theoretic aspects of quantum groups (16T20) Cluster algebras (13F60)

Related Items

Spectra of quantum KdV Hamiltonians, Langlands duality, and affine opers ⋮ The periodicity conjecture for pairs of Dynkin diagrams ⋮ Cluster algebras ⋮ Monoidal categorification and quantum affine algebras. II ⋮ Periodicities of T-systems and Y-systems, dilogarithm identities, and cluster algebras. I: Type \(B_r\) ⋮ Periodicities of T-systems and Y-systems, dilogarithm identities, and cluster algebras. II: Types \(C_r, F_4\), and \(G_2\) ⋮ Rogers-Ramanujan type identities and nil-DAHA ⋮ Extended T-systems ⋮ Cluster realization of Weyl groups and \(q\)-characters of quantum affine algebras ⋮ 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 ⋮ Quiver varieties and cluster algebras ⋮ A monoidal category for perturbed defects in conformal field theory ⋮ Cluster algebras and quantum affine algebras ⋮ Thermodynamics of the topological Kondo model ⋮ Difference equations arising from cluster algebras ⋮ Generators of rank 2 cluster algebras of affine types via linearization of seed mutations ⋮ Synchronicity phenomenon in cluster patterns ⋮ Quantum periodicity and Kirillov-Reshetikhin modules ⋮ T-functions and multi-gluon scattering amplitudes

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Conformal weights of RSOS lattice models and their fusion hierarchies
• Cluster categories for algebras of global dimension 2 and quivers with potential.
• Cluster characters for 2-Calabi-Yau triangulated categories.
• Cluster algebras of finite type via Coxeter elements and principal minors.
• \(Q\)-systems as cluster algebras. II: Cartan matrix of finite type and the polynomial property
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Eight-vertex SOS model and generalized Rogers-Ramanujan-type identities
• Solvable lattice models related to the vector representation of classical simple Lie algebras
• Etiology of IRF models
• Quantum affine algebras
• Quantum integrable models and discrete classical Hirota equations
• Cluster algebras. II: Finite type classification
• \(Y\)-systems and generalized associahedra
• Identities for the Rogers dilogarithm function connected with simple Lie algebras
• The canonical solutions of the \(Q\)-systems and the Kirillov-Reshetikhin conjecture
• The \(q\)-characters at roots of unity
• Spectra of tensor products of finite dimensional representations of Yangians
• Thermodynamic Bethe ansatz and dilogarithm identities. I.
• The periodicity conjecture for pairs of Dynkin diagrams
• Cluster mutation via quiver representations.
• A periodicity theorem for the octahedron recurrence
• On the periodicity conjecture for \(Y\)-systems
• Mutation in triangulated categories and rigid Cohen-Macaulay modules
• From triangulated categories to cluster algebras
• Cluster algebras as Hall algebras of quiver representations.
• Tilting theory and cluster combinatorics.
• Quiver varieties and \(t\)-analogs of \(q\)-characters of quantum affine algebras
• Making diagrams speak, in Bhāskara I's commentary on the \textit{Āryabhaṭīya}
• On triangulated orbit categories
• SPECTRA IN CONFORMAL FIELD THEORIES FROM THE ROGERS DILOGARITHM
• FUNCTIONAL RELATIONS IN SOLVABLE LATTICE MODELS I: FUNCTIONAL RELATIONS AND REPRESENTATION THEORY
• FUNCTIONAL RELATIONS IN SOLVABLE LATTICE MODELS II: APPLICATIONS
• THERMODYNAMIC BETHE ANSATZ AND THREE-FOLD TRIANGULATIONS
• Cluster algebras I: Foundations
• Nonlinear Partial Difference Equations. II. Discrete-Time Toda Equation
• Monoidal Categorifications of Cluster Algebras of Type A and D
• Cluster algebras, quiver representations and triangulated categories
• A TOPOLOGICAL INVARIANT OF RG FLOWS IN 2D INTEGRABLE QUANTUM FIELD THEORIES
• Cluster structures for 2-Calabi–Yau categories and unipotent groups
• Kirillov-Reshetikhin Conjecture: The General Case
• The Kirillov-Reshetikhin conjecture and solutions of T-systems
• Cluster algebras IV: Coefficients
• From triangulated categories to cluster algebras II
• Restricted solid-on-solid models connected with simply laced algebras and conformal field theory
• Q-systems as cluster algebras
• On the Combinatorics of Rigid Objects in 2-Calabi-Yau Categories
• Quantum Jacobi-Trudi and Giambelli formulae for U_q(B_r⁽¹⁾) from the analytic Bethe ansatz
• Quiver varieties and finite dimensional representations of quantum affine algebras
• DifferenceLoperators related toq-characters
• Functional relations and analytic Bethe ansatz for twisted quantum affine algebras
• Combinatorics of \(q\)-characters of finite-dimensional representations of quantum affine algebras.