Abstract
Studying the algebraic structure of the doubleDY(g) of the Yangian Y(g), we present the triangular decomposition ofDY(g) and a factorization for the canonical pairing of the Yangian with its dual inside Y0(g). As a consequence, we describe a structure of the universalR-matrixR forDY(g) which is complete forDY(s12). We demonstrate how this formula works in evaluation representations of Y(sl2). We interpret the one-dimensional factor arising in concrete representations ofR as a bilinear form on highest-weight polynomials of irreducible representations of Y(g) and express this form in terms of Γ-functions.
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Partially supported by ISF grant MBI000 and Russian Foundation for Fundamental Researches
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Khoroshkin, S.M., Tolstoy, V.N. Yangian double. Lett Math Phys 36, 373–402 (1996). https://doi.org/10.1007/BF00714404
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DOI: https://doi.org/10.1007/BF00714404