Yangians and transvector algebras

Olshanski' s centralizer construction provides a realization of the Yangian Y(m) for the Lie algebra gl(m) as a subalgebra in the projective limit algebra A m = lim proj A m (n) as n → ∞, where A m (n) is the centralizer of gl(n − m) in the enveloping algebra U(gl(n)). We give a modified version of this construction based on a quantum analog of Sylvester's theorem. We then use it to get an algebra homomorphism from the Yangian Y(n) to the transvector algebra associated with the pair gl(m) ⊂ gl(m + n). The results are applied to identify the elementary representations of the Yangian by constructing their highest vectors explicitly in terms of elements of the transvector algebra.