Abstract
Explicit formulas of the universalR-matrix are given for all quantized nontwisted rank 3 affine KM algebras U q (A (1)2 ), U q (C (1)2 ) and U q (G (1)2 ).
Similar content being viewed by others
References
Kac, V. G.,Infinite Dimensional Lie Algebras, Progr. Math.44, Birkhäuser, Boston, Basel, Stuttgart, 1983.
Drinfeld, V. G.,Proc. ICM, Berkeley 1 (1986) 798.
Jimbo, M.,Lett. Math. Phys. 10, 63 (1985),11, 247 (1986).
Alvarez-Gaumé, L., Gomes, C., and Sierra, G.,Phys. Lett. B 220, 142 (1989);Nuclear Phys. B319, 155 (1989); Moore, G. and Reshetikhin, N. Yu.,Nuclear Phys. B328, 557 (1989).
Faddeev, L. D., Integrable models in (1 + 1)-dimensional quantum field theory, inRecent Advances in Field Theory and Statistical Mechanics, North-Holland, Amsterdam, 1984, p. 563.
Baxter, R. J.,Exactly Solved Models in Statistical Mechanics, Academic Press, New York, 1982.
Witten, E.,Comm. Math. Phys. 121, 351 (1989).
Reshetikhin, N., Quantized universal enveloping algebras, the Yang-Baxter equation and invariants of links: I, II, Preprints LOMI E-4-87, E-17-87.
Zhang, R. B., Gould, M. D., and Bracken, A. J.,Comm. Math. Phys. 137, 13 (1991); Links, J. R., Gould, M. D., and Zhang, R. B., Quantum supergroups, link polynomials and representation of the braid generator, The University of Queensland preprint, 1992.
Rosso, M.,Comm. Math. Phys. 124, 307 (1989).
Kirillov, A. N. and Reshetikhin, N.,Comm. Math. Phys. 134, 421 (1991).
Khoroshkin, S. M. and Tolstoy, U. N.,Comm. Math. Phys. 141, 599 (1991).
Khoroshkin, S. M. and Tolstoy, U. N., The universalR-matrix for quantized nontwisted affine Lie algebras, inProc. 4th Workshop, Obniusk, 1990, to appear inFunktsional Anal. i Prilozhen.
Zhang, Y.-Z. and Gould, M. D., Unitarity and complete reducibility of certain modules over quantized affine KM algebras, The University of Queensland preprint, UQMATH-93-02, 1993.
Jimbo, M.,Comm. Math. Phys. 102, 247 (1986).
Zhang, R. B., Gould, M. D., and Bracken, A. J.,Nuclear Phys. B354, 625 (1991).
Kuniba, A.,J. Phys. Math. Gen. A23, 1349 (1990).
Zhang, Y.-Z. and Gould, M. D., Quantum affine algebras and universalR-matrix with spectral parameter: I, II, Preprints UQMATH-93-05, hep-th/9307007 and UQMATH-93-06, hep-th/9307008.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Zhang, Y.Z., Gould, M.D. On universalR-matrix for quantized nontwisted rank 3 affine KM algebras. Lett Math Phys 29, 19–31 (1993). https://doi.org/10.1007/BF00760855
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00760855