Irreducible representations of Yangians

TL;DR

This paper provides explicit constructions of irreducible representations for Yangians related to general linear, symplectic, and orthogonal Lie algebras, and develops a fusion procedure for twisted Yangians, extending Cherednik's work.

Contribution

It introduces explicit realizations of irreducible Yangian representations and develops the fusion procedure for twisted Yangians, expanding prior theoretical frameworks.

Findings

Explicit realizations of irreducible Yangian representations

Development of fusion procedure for twisted Yangians

Extension of Cherednik's fusion work to twisted cases

Abstract

We give explicit realizations of irreducible representations of the Yangian of the general linear Lie algebra and of its twisted analogues, corresponding to symplectic and orthogonal Lie algebras. In particular, we develop the fusion procedure for twisted Yangians. For the non-twisted Yangian, this procedure goes back to the works of Cherednik.