Yangians and transvector algebras


A. I. Molev


Research Report 98-30
Date: 19 November 1998


Olshanski's centralizer construction provides a realization of the Yangian for the general linear Lie algebra as a subalgebra in the projective limit of a chain of centralizers in the universal enveloping algebras. 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 to the transvector algebra associated with the general linear Lie algebras. 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.

Key phrases

Yangian. transvector algebra. elementary representation. Drinfeld polynomials.

AMS Subject Classification (1991)

Primary: 17B35
Secondary: 81R50


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