Quantum Orbit Method in the Presence of Symmetries

Abstract

We review some of the main achievements of the orbit method, when applied to Poisson–Lie groups and Poisson homogeneous spaces or spaces with an invariant Poisson structure. We consider C∗-algebra quantization obtained through groupoid techniques, and we try to put the results obtained in algebraic or representation theoretical contexts in relation with groupoid quantization.

Keywords

• orbit method
• symplectic groupoid
• geometric quantization
• Poisson-Lie group