Quantized affine Lie algebras and diagonalization of braid generators |
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Authors: | M D Gould Y -Z Zhang |
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Institution: | (1) Department of Mathematics, University of Queensland, Brisbane, 4072 Qld, Australia |
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Abstract: | Let U
q
be a quantized affine Lie algebra. It is proven that the universal R-matrix R of U
q
satisfies the celebrated conjugation relationR
+ =TR withT the usual twist map. As applications, the braid generator is shown to be diagonalizable on arbitrary tensor product modules
of integrable irreducible highest weight U
q
-module and a spectral decomposition formula for the braid generator is obtained which is the generalization of Reshetikhin
and Gould forms to the present affine case. Casimir invariants are constructed and their eigenvalues computed by means of
the spectral decomposition formula. As a by-product, an interesting identity is found. |
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Keywords: | 81R10 17B37 16W30 |
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