Orthogonal and symplectic Yangians - linear and quadratic evaluations

TL;DR

This paper investigates the conditions under which simple linear or quadratic L operators exist for orthogonal and symplectic Yangians, expanding understanding of their algebraic structures and representations.

Contribution

It provides a general analysis of the restrictive conditions necessary for the existence of simple L operators in orthogonal and symplectic Yangians.

Findings

Identifies conditions for linear L operators in Yangians.

Identifies conditions for quadratic L operators in Yangians.

Clarifies algebraic structures of orthogonal and symplectic Yangians.

Abstract

Orthogonal or symplectic Yangians are defined by the Yang-Baxter $RLL$ relation involving the fundamental $R$ matrix with $so(n)$ or $sp(2m)$ symmetry. Simple $L$ operators with linear or quadratic dependence on the spectral parameter exist under restrictive conditions. These conditions are investigated in general form.