Representations of orthogonal and symplectic Yangians

TL;DR

This paper explores the structure and representations of extended Yangian algebras associated with orthogonal and symplectic groups, providing explicit L-operator constructions and analyzing their representation conditions.

Contribution

It introduces new representations of extended Yangian algebras using Clifford and Heisenberg algebras and characterizes their properties and constraints.

Findings

Derived explicit L-operator expressions for these Yangians.

Analyzed conditions on representation weights for linear and quadratic evaluations.

Characterized representations using underlying algebraic structures.

Abstract

Exteded Yangian algebras of orthogonal and symplectic types are defined by the Yang-Baxter RLL relation involving the fundamental R-matrix with $so(n)$ or $sp(2m)$ symmetry. We study representations of highest weight characterized by weight function ratios. We consider the algebra relations for the linear and the quadratic evaluations and the resulting conditions imposed on the representation weights. We present expressions of L-operators constructed on underlying Clifford and Heisenberg algebras and characterize their representations.