Abstract
Aq-difference analogue of the universal envelo** algebra U(g) of a simple Lie algebra g is introduced. Its structure and representations are studied in the simplest case g=sl(2). It is then applied to determine the eigenvalues of the trigonometric solution of the Yang-Baxter equation related to sl(2) in an arbitrary finite-dimensional irreducible representation.
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References
KulishP. P. and ReshetikhinN. Yu.,J. Soviet Math. 23, 2435 (1983). Russian originalZapiski nauch. semin. LOMI 101, 112 (1980).
KulishP. P. and SklyaninE. K.,J. Soviet Math. 19, 1596 (1982). Russian originalZapiski nauch. semin. LOMI 95, 129 (1980).
KulishP. P., ReshetikhinN. Yu., and SklyaninE. K.,Lett. Math. Phys. 5, 393 (1981).
KacV. G.,Infinite Dimensional Lie Algebras, Birkhäuser, Boston, 1983.
Andrews, G. E.,The Theory of Partitions, Addison-Wesley, 1976.
Jimbo, M., RIMS preprint506 (1985), to appear inCommun. Math. Phys.
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Jimbo, M. Aq-difference analogue of U(g) and the Yang-Baxter equation. Lett Math Phys 10, 63–69 (1985). https://doi.org/10.1007/BF00704588
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DOI: https://doi.org/10.1007/BF00704588