T-systems and Y-systems in integrable systems
T-systems and Y-systems in integrable systems
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DOI：
10.1088/1751-8113/44/10/103001
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发表时间：
2010-10
期刊：
影响因子：
--
通讯作者：
A. Kuniba;T. Nakanishi;J. Suzuki
中科院分区：
文献类型：
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作者：
A. Kuniba;T. Nakanishi;J. Suzuki
T系统和Y系统是经典和量子可积系统中普遍存在的结构。它们是具有与可解晶格模型中可交换转移矩阵相关的各个方面的差分方程、量子仿射代数的Kirillov-Reshetikhin模的q特征、具有系数的簇代数、Zamolodchikov等人的周期性猜想、共形场论中的双对数等式、KP族中L-算子的差分模拟、1D薛定谔问题中的斯托克斯现象、AdS/CFT对应、离散时空中的户田场方程、离散几何中的拉普拉斯序列、Bethe变换的费米特征公式和组合完备性、Q系统和理想气体的不相容统计、解析和热力学Bethe变换、量子转移矩阵方法等。这篇评论是关于这些主题的简短评论的集合，可以或多或少独立阅读。
T- and Y-systems are ubiquitous structures in classical and quantum integrable systems. They are difference equations having a variety of aspects related to commuting transfer matrices in solvable lattice models, q-characters of Kirillov–Reshetikhin modules of quantum affine algebras, cluster algebras with coefficients, periodicity conjectures of Zamolodchikov and others, dilogarithm identities in conformal field theory, difference analog of L-operators in KP hierarchy, Stokes phenomena in 1D Schrödinger problem, AdS/CFT correspondence, Toda field equations on discrete spacetime, Laplace sequence in discrete geometry, Fermionic character formulas and combinatorial completeness of Bethe ansatz, Q-system and ideal gas with exclusion statistics, analytic and thermodynamic Bethe ansätze, quantum transfer matrix method and so forth. This review is a collection of short reviews on these topics which can be read more or less independently.