T-systems and Y-systems in integrable systems

Details T-systems and Y-systems in integrable systems T-systems and Y-systems in integrable systems

2010-10-07

arxiv.org/abs/1010.1344v3

J.Phys.A44:103001,2011

Physics

High Energy Physics

High Energy Physics - Theory

156 pages, minor adjustments along the published version (JPA: Topical Review)

Scientific paper

10.1088/1751-8113/44/10/103001

The 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 analogue of L-operators in KP hierarchy, Stokes phenomena in 1d Schr\"odinger problem, AdS/CFT correspondence, Toda field equations on discrete space-time, 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 ans\"atze, quantum transfer matrix method and so forth. This review article is a collection of short reviews on these topics which can be read more or less independently.

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