The restricted quantum double of the Yangian

Let g be a complex semisimple Lie algebra with associated Yangian Yg . In the mid-1990s, Khoroshkin and Tolstoy formulated a conjecture which asserts that the algebra DYg obtained by doubling the generators of Yg , called the Yangian double, provides a realization of the quantum double of the Yangian. We provide a uniform proof of this conjecture over C[-1.2pt\![ ]\!-1.2pt] which is compatible with the theory of quantized enveloping algebras. As a by-product, we identify the universal R -matrix of the Yangian with the canonical element defined by the pairing between the Yangian and its restricted dual.