Abstract
It is now well known that the topology of knots in Euclidean 3-space is closely related to the study of the quantum Yang-Baxter equation R12R23R12=R23R12R23 (O.a) where R is an endomorphism of V ⊗ V for a vector space V.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
R. J. Baxter, Exactly Solved Models in Statistical Mechanics, Academic Press, 1982
G. Gasper, M. Rahman, Basic Hypergeometric Series, Cambridge Univ. Press, 1990
E. Date, M. Jimbo, T. Miwa, M. Okado, Fusion of the eight-vertex SOS model, Lett. Math. Phys. 12 (1986), 209–215. Erratum and Addendum: Lett. Math. Phys. 14 (1987), 97
I. B. Frenkel, V. G. Turaev, Elliptic solutions of the Yang-Baxter equation and modular hypergeometric functions, to appear
M. Jimbo, Solvable lattice models and quantum groups, Proceedings of the ICM, Kyoto, Japan, 1990, Springer-Verlag, 1343–1352
V.F.R. Jones, Index for subfactors, Invent. Math. 72 (1983), 1–25
L. Kauffman, S.L. Lins, Temperley-Lieb recoupling theory and invariants of 3-manifolds, Princeton Univ. Press, Princeton, N.J. 1994
A.N. Kirillov, N.Y. Reshetikhin, Representations of the algebra Uq(sl2), q-orthogonal polynomials and invariants of links. In: Infinite dimensional Lie algebras and groups, (ed. V.G. Kac), 285-339. Adv. Ser. In Math. Phys. 7, World Scientific, Singapore 1988
P.P. Kulish, N.Y. Reshetikhin, E.K. Sklyanin, Yang-Baxter equation and representation theory, I. Lett. Math. Phys. 5 (1981), 393–403
G. Masbaum, P. Vogel, 3-valent graphs and the Kauffman bracket, Pac. J. Math. 164 (1994), 361–381
V. G. Turaev, Quantum Invariants of Knots and 3-Manifolds, de Gruyter Studies in Math. 18, 1994
H. Wenzl, On sequences of projections, C. R. Math. Rep. Acad. Sci. Canada 9, n. 1 (1987), 5–9
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Additional information
Dedicated to Israel Moiseevich Gelfand on his 80th birthday
Rights and permissions
Copyright information
© 1995 Birkhäuser Boston
About this chapter
Cite this chapter
Frenkel, I.B., Turaev, V.G. (1995). Trigonometric Solutions of the Yang-Baxter Equation, Nets, and Hypergeometric Functions. In: Gindikin, S., Lepowsky, J., Wilson, R.L. (eds) Functional Analysis on the Eve of the 21st Century. Progress in Mathematics, vol 131. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4262-8_3
Download citation
DOI: https://doi.org/10.1007/978-1-4612-4262-8_3
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-8713-1
Online ISBN: 978-1-4612-4262-8
eBook Packages: Springer Book Archive