Principal Realization of the Yangian Y(gl(n))

TL;DR

This paper introduces a new principal realization for the Yangian Y(gl(n)), simplifying tensor representations and the Yangian action, with an explicit isomorphism to the standard basis.

Contribution

It provides a novel principal basis for Y(sl(n)) and demonstrates its effectiveness in simplifying tensor actions compared to traditional bases.

Findings

Principal basis simplifies Yangian tensor actions

Explicit isomorphism to Cartan-Weyl basis established

Enhanced understanding of Yangian structure in Lie algebras

Abstract

Motivated to simplify the structure of tensor representations we give a new set of generators for the Yangian $Y(sl(n))$ using the principal realization in simple Lie algebras. The isomorphism between our new basis and the standard Cartan-Weyl basis is also given. We show by example that the principal basis simplifies the Yangian action significantly in the tensor product of the fundamental representation and its dual.