An Introduction to Yangian Symmetries

Abstract

We review some aspects of the quantum Yangians as symmetry algebras of two-dimensional quantum field theories. The plan of these notes is the following: 1 - The classical Heisenberg model: Non-Abelian symmetries; The generators of the symmetries and the semi-classical Yangians; An alternative presentation of the semi-classical Yangians; Digression on Poisson-Lie groups. 2 - The quantum Heisenberg chain: Non-Abelian symmetries and the quantum Yangians; The transfer matrix and an alternative presentation of the Yangians; Digression on the double Yangians. Talk given at the "Integrable Quantum Field Theories" conference held at Come, Italy , September 13-19, 1992.