Yangian double
The authors study the algebraic structure of the quantum double \(D\) of a Yangian \(Y(g)\) and conjecture a description of it in terms of generators and relation (this conjecture is proved when \(g=\text{sl}_2)\). A triangular decomposition of \(D\) is given along with a factorization of the canonical pairing of \(Y(g)\) with its Hopf dual inside \(D\). A factorization theorem for the universal \(R\)-matrix of \(D\) is deduced, and made explicit in the \(\text{sl}_2\) case with a conjectural formula for the \(R\)-matrix in the general case. The action of the \(R\)-matrix in tensor products of evaluation representations is computed.
scientific article; zbMATH DE number 878270