Fusion, mass, and representation theory of the Yangian algebra

Abstract

Based on the formulation of Drinfel'd, Chari, and Pressley, a technique to analyze the structure of tensor products of the Yangian algebra representations is presented. We then apply the results to the $S$-matrix theory of the $G\otimes G$-invariant nonlinear $\sigma$-model ($G$-principal chiral model) by Ogievetsky, Reshetikhin, and Wiegmann. We show how the physical data such as mass formula, fusion angle, and the spins of integrals of motion can be extracted from the Yangian highest weight representations.

22 pages, 1 ps figure; psbox (included),harvmac, (minor revision, but replacement recommended) HUTP-94/A010; v3: TeX compiling problem is fixed, no change of contents

References in corpus (5)

• Yang-Baxter equation in spin chains with long range interactions
• Exact S-Matrices for Nonsimply-Laced Affine Toda Theories
• Root Systems and Purely Elastic S-Matrices II
• A remark on the coupling-dependence in affine Toda field theories
• The full set of $c_n$-invariant factorized $S$-matrices

Cited by in corpus (3)

• Introduction to Yangian symmetry in integrable field theory
• Local Weyl modules and cyclicity of tensor products for Yangians
• Systematic proof of the existence of Yangian symmetry in chiral Gross-Neveu models