2010/10/31 by Atsuo Kuniba, Tomoki Nakanishi, Junji Suzuki · 1 citation
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.MP #math.QA #nlin.SI #msc:82B23 #msc:16T25 #msc:81R50
paper · pdf · doi:10.1088/1751-8113/44/10/103001
published as J.Phys.A44:103001,2011 · 156 pages. Minor corrections including the last paragraph of sec.3.5, eqs.(4.1), (5.28), (9.37) and (13.54). The published version (JPA topical review) also needs these corrections
arxiv created 2014/06/06 · arxiv updated 2014/06/09
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 Schrödinger 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 ansätze, 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.