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We study geometric consistency relations between angles on 3-dimensional (3D) circular quadrilateral lattices -- lattices whose faces are planar quadrilaterals inscribable into a circle.
Leçons sur les systémes orthogonaux et les coordonnées curvilignes
Darboux, G · 1910
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Generalized Volume Conjecture and the A-Polynomials – the Neumann-Zagier Potential Function as a Classical Limit of Quantum Invariant
Hikami, K · 1940
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Some exact results for the many-body problem in one dimension with repulsive delta-function interaction
Yang, C. N · 1967
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Partition function of the eight-vertex lattice model
Baxter, R. J · 1972
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Tetrahedra equations and integrable systems in three-dimensional space
Zamolodchikov, A. B · 1980
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Tetrahedron equations and the relativistic S matrix of straight strings in (2+1)-dimensions
Zamolodchikov, A. B · 1981
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Hyperbolic geometry: the first 150 years
Milnor, J · 1982
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Infinite conformal symmetry in two-dimensional quantum field theory
Belavin, A. A., Polyakov, A. M., and Zamolodchikov, A. B · 1984
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A q q -difference analogue of U ( G ) {U}({G}) and the Yang-Baxter equation
Jimbo, M · 1985
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Construction of multidimensional nonlinear integrable systems and their solutions
Zakharov, V. E. and Manakov, S. V · 1985
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Trigonometric solution of triangle equations and classical Lie algebras
Bazhanov, V. V · 1985
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The Yang-Baxter Equations and the Zamolodchikov Model
Baxter, R. J · 1986
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Quantum R R matrix for the generalized Toda system
Jimbo, M · 1986
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Quantum groups
Drinfel’d, V. G · 1987
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Quantum triangle equations and simple Lie-superalgebras
Bazhanov, V. V. and Shadrikov, A. G · 1987
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Quantum field theory and the Jones polynomial
Witten, E · 1989
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( Z N × ) n − 1 ({Z}_{N}\times)^{n-1} generalization of the chiral Potts model
Bazhanov, V. V., Kashaev, R. M., Mangazeev, V. V., and Stroganov, Y. G · 1991
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Generalized chiral Potts models and minimal cyclic representations of U q ( g l ( n , C ) ) {U}_{q}(gl(n,{C}))
Date, E., Jimbo, M., Miki, K., and Miwa, T · 1991
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Invariants of 3 3 -manifolds via link polynomials and quantum groups
Reshetikhin, N. and Turaev, V. G · 1991
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Quantum Volterra model
Volkov, A. Y · 1992
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New solvable lattice models in three-dimensions
Bazhanov, V. V. and Baxter, R. J · 1992
Cited alongside, same era.
State sum invariants of 3 3 -manifolds and quantum 6 j 6j -symbols
Turaev, V. G. and Viro, O. Y · 1992
Cited alongside, same era.
Abelian current algebra and the Virasoro algebra on the lattice
Faddeev, L. and Volkov, A. Y · 1993
Cited alongside, same era.
Star triangle relation for a three-dimensional model
Bazhanov, V. V. and Baxter, R. J · 1993
Cited alongside, same era.
Spatial symmetry, local integrability and tetrahedron equations in the Baxter-Bazhanov model
Kashaev, R. M., Mangazeev, V. V., and Stroganov, Y. G · 1993
Cited alongside, same era.
Tetrahedral Zamolodchikov algebras corresponding to Baxter’s L {L} -operators
Korepanov, I. G · 1993
Cited alongside, same era.
Quantization of Teichmüller spaces and the quantum dilogarithm
Kashaev, R. M · 1998
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Discrete conformal maps and surfaces
Bobenko, A. I · 1999
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Liouville bootstrap via harmonic analysis on a noncompact quantum group
Ponsot, B. and Teschner, J · 1999
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Quantum Teichmüller spaces
Fok, V. V. and Chekhov, L. O · 1999
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The symmetric, d d -invariant and Egorov reductions of the quadrilateral lattice
Doliwa, A. and Santini, P. M · 2000
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Modular double of a quantum group
Faddeev, L · 2000
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Lattice and q q -difference Darboux-Zakharov-Manakov systems via ∂ ¯ \overline{\partial} -dressing method
Bogdanov, L. V. and Konopelchenko, B. G · 1995
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Discrete Heisenberg-Weyl group and modular group
Faddeev, L. D · 1995
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A link invariant from quantum dilogarithm
Kashaev, R. M · 1995
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Currentlike variables in massive and massless integrable models
Faddeev, L · 1996
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Discrete isothermic surfaces
Bobenko, A. and Pinkall, U · 1996
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On discrete three-dimensional equations associated with the local Yang-Baxter relation
Kashaev, R · 1996
Cited alongside, same era.
Murakami, H. and Murakami, J · 2001
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Ponsot, B. and Teschner, J · 2001
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Menelaus’ theorem, Clifford configurations and inversive geometry of the Schwarzian KP hierarchy
Konopelchenko, B. G. and Schief, W. K · 2002
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Circle packing: a mathematical tale
Stephenson, K · 2003
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Classification of integrable equations on quad-graphs. The consistency approach
Adler, V. E., Bobenko, A. I., and Suris, Y. B · 2003
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Variational principles for circle patterns and Koebe’s theorem
Bobenko, A. I. and Springborn, B. A · 2004
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Discrete differential geometry. Consistency as integrability, 2005
Bobenko, A. I. and Suris, Y. B · 2005
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Zamolodchikov’s tetrahedron equation and hidden structure of quantum groups
Bazhanov, V. V. and Sergeev, S. M · 2006
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Faddeev-Volkov solution of the Yang-Baxter Equation and Discrete Conformal Symmetry
Bazhanov, V. V., Mangazeev, V. V., and Sergeev, S. M · 2007
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On discretization principles for differential geometry. The geometry of spheres
Bobenko, A. I. and Suris, Y. B · 2007
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Hidden Grassmann structure in the X X Z XXZ model
Boos, H., Jimbo, M., Miwa, T., Smirnov, F., and Takeyama, Y · 2007
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Exact solution of the Faddeev-Volkov model
Bazhanov, V. V., Mangazeev, V. V., and Sergeev, S. M · 2008
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Integrable Systems and Quantum Discrete Geometry
Bazhanov, V. V., Mangazeev, V. V., and Sergeev, S. M · 2008
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