The uniqueness theorem for the universal R-matrix |
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Authors: | S M Khoroshkin V N Tolstoy |
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Institution: | (1) Institute of New Technologies, Kirovogradskaya 11, 113587 Moscow, Russia;(2) Institute of Nuclear Physics, Moscow State University, 119899 Moscow, Russia |
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Abstract: | Up to now, the universal R-matrix for quantized Kac-Moody algebras is believed to be uniquely determined (for some ansatz) by properties of a quasi-cocommutativity and a quasi-triangularity. We prove here that the universal R-matrix (for the same ansatz) is uniquely determined by the property of the quasi-cocommutativity only. Thus, the quasi-triangular property (and the Yang-Baxter equation!) for the universal R-matrix is a consequence of the linear equation of the quasi-cocommutativity. The proof is based on properties of singular vectors in the tensor product of the Verma modules and the structure of extremal projector for quantized algebras. Explicit expressions of the universal R-matrix for quantized algebras U
q
(A
inf1
sup(1)
) and U
q
(A
inf2
sup(2)
) are given.
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Keywords: | 81R10 17B37 16W30 |
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