Central Extension of the Yangian Double

TL;DR

This paper introduces the central extension of the Yangian double for simple Lie algebras, providing a complete proof for sl_2 and constructing basic representations and intertwining operators.

Contribution

It defines the central extension of the Yangian double and develops foundational representation theory for the case of sl_2.

Findings

Complete proof of the central extension for sl_2

Construction of basic representations for DY2

Development of intertwining operators

Abstract

Central extension $\DYg$ of the Double of the Yangian is defined for a simple Lie algebra ${\bf g}$ with complete proof for ${\bf g} =sl_2$. Basic representations and intertwining operators are constructed for $\DY2$.