Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 44, Issue 10, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/44/10/103001
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Funding
- JSPS [21540209, 20540370]
- Grants-in-Aid for Scientific Research [21540209, 20540370] Funding Source: KAKEN
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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 Schrodinger 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 ansatze, 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.
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