Yangian Double and Rational R-matrix

Abstract

Studying the algebraic structure of the double $\mathcal{D}Y(g)$ of the yangian $Y(g)$ we present the triangular decomposition of $\mathcal{D}Y(g)$ and a factorization for the canonical pairing of the yangian with its dual inside $\mathcal{D}Y(g)$. As a consequence we obtain an explicit formula for the universal R-matrix $R$ of $\mathcal{D}Y(g)$ and demonstrate how it works in evaluation representations of $Y(s{l}_2)$. We interprete one-dimensional factor arising in concrete representations of $R$ as bilinear form on highest weight polynomials of irreducible representations of $Y(g)$ and express this form in terms of {\it gamma-functions}.

25 pages

References in corpus (1)

• Gauss decomposition of trigonometric R-matrices

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