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Quantum affine algebras

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Abstract

We classify the finite-dimensional irreducible representations of the quantum affine algebra\(U_q (\hat sl_2 )\) in terms of highest weights (this result has a straightforward generalization for arbitrary quantum affine algebras). We also give an explicit construction of all such representations by means of an evaluation homomorphism\(U_q (\hat sl_2 ) \to U_q (sl_2 )\), first introduced by M. Jimbo. This is used to compute the trigonometricR-matrices associated to finite-dimensional representations of\(U_q (\hat sl_2 )\).

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Authors and Affiliations

  1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, 5, Bombay, India

    Vyjayanthi Chari

  2. Department of Mathematics, King's College, Strand, WC2R 2LS, London, England, UK

    Andrew Pressley

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  1. Vyjayanthi Chari
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  2. Andrew Pressley
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Communicated by J. Fröhlich

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Chari, V., Pressley, A. Quantum affine algebras. Commun.Math. Phys. 142, 261–283 (1991). https://doi.org/10.1007/BF02102063

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  • DOI: https://doi.org/10.1007/BF02102063

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