On the quantization of polygon spaces

Understand

Moduli spaces of polygons have been studied since the nineties for their topological and symplectic properties.

• Under generic assumptions, these are symplectic manifolds with natural global action-angle coordinates.
• This paper is concerned with the quantization of these manifolds and of their action coordinates.
• Applying the geometric quantization procedure, one is lead to consider invariant subspaces of a tensor product of irreducible representations of SU(2).