# 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

## Content

The paper is available in the following forms:
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- 1998-30.dvi.gz (39kB) or
1998-30.dvi (101kB)

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