Abstract
TheR-matrices for the quantised Lie algebrasA n are constructed through the quantum double procedure given by Drinfel'd [6]. The case ofU q sl(3) is thoroughly analysed initially to demonstrate the more subtle points of the calculation. The ease of the calculation forA n is very dependent on a choice of generators for the Borel subalgebraU q b + and its dual, and a certain ordering imposed on these generators which is related to the length of a certain word in the Weyl group.
Similar content being viewed by others
References
Babelon, O.: Extended conformal algebra and the Yang baxter equation. Phys. LettB215, 523 (1988)
Belavin, A. A., Drinfeld, V. G.: Triangle equations and simple Lie algebras. Sov. Sci. Rev., Sect.C4, 93–165 (1984)
Bernard, D.: Vertex operator representations of the Quantum Affine AlgebraU q (B r (1)). Meudon preprint No. 88068 1988
Burroughs, N.: In preparation
Burroughs, N.: In preparation
Drinfeld, V. G.: Quantum groups. ICM Berkeley 1986. Gleason, A. M. (ed.). AMS, Providence 798 (1987)
Exton, H.:Q-hypergeometric functions and applications. Ellis Horwood Series: Mathematics and its Applications 1983
Faddeev, L.: Integrable models in (1+1)-dimensional Quantum Field Theory. Les Houches Summer School 1982
Fadeev, L., Reshtikhin, N., Takhtajan, L.: Quantisation of Lie groups and Lie algebras. Leningrad preprint LOMI E-14-87
Humphreys, J.E.: Introduction to Lie algebras and Representation theory. Berlin, Heidelberg, New York: Springer 1980
Jimbo, M.: Aq-analogue of theU q (gl(N+1)), Hecke Algebra, and the Yang-Baxter Equation. Lett. Math. Phys.11, 247–252 (1986)
Jimbo, M.: QuantumR matrix for the generalised Toda system. Commun. Math. Phys.102, 537–547 (1986)
Kosmann-Schwarzbach, Y.: Poisson Drinteld groups. Appears in topics in Sliton theory and exactly solvable nonlinear equations. Ablowitz, M., Fuchssteiner, B., Kruskal, M. (eds.). Singapore: World Scientific 1987
Kulish, P. P., Reshetikhin, N. Y., Skylanin, E. K.: Yang Baxter equation and representation theory: 1. Lett. Math. Phys.5, 393–403 (1981)
Lawrence, R. J.: A universal link invariant using quantum groups. Oxford preprint. (Mathematical Institute.)
Moore, G., Seiberg, N.: Classical and quantum conformal field theory. IAS preprint IASSNS-HEP-88/39
Skylanin, E. K.: New approach to the quantum nonlinear Schrödinger equation. Freiburg preprint THEP 89/2
Skylanin, E. K.: Exact quantisation of the sinh-Gordon model. Freiburg preprint THEP 89/3
Smit, D. J.: The quantum group structure of conformal field theories. Utrecht preprint THU 88-33
Author information
Authors and Affiliations
Additional information
Communicated by J. Fröhlich
Supported by a SERC studentship
Rights and permissions
About this article
Cite this article
Burroughs, N. The universalR-matrix forU q sl(3) and beyond!. Commun.Math. Phys. 127, 109–128 (1990). https://doi.org/10.1007/BF02096496
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02096496