Mickelsson algebras and representations of Yangians

TL;DR

This paper leverages Howe's reductive dual pairs to explicitly realize irreducible representations of Yangians and twisted Yangians associated with classical Lie algebras, advancing the understanding of their structure.

Contribution

It introduces explicit constructions of irreducible Yangian and twisted Yangian representations using Howe's dual pairs, a novel approach in the field.

Findings

Explicit realizations of Yangian representations

Explicit realizations of twisted Yangian representations

Enhanced understanding of Yangian structures

Abstract

We use the theory of reductive dual pairs due to Howe to obtain explicit realizations of irreducible representations of the Yangian of the general linear Lie algebra, and of the twisted Yangians corresponding to the symplectic and orthogonal Lie algebras.