Yangians and transvector algebras
Author
A. I. Molev
Status
Research Report 98-30
Date: 19 November 1998
Abstract
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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