Dunkl Operator Formalism for Quantum Many-Body Problems Associated with Classical Root Systems

Abstract

The integrable quantum many-body systems associated withthe classical root systems are formulated in terms of the(trigonometric) Dunkl operators.We define the Dunkl operators by use of the infinite-dimensionalrepresentation of the R and K matrices for the Yang-Baxterequation and the reflection equation.The eigenvalues of systems are also given.