Quantisation of bending flows

Abstract

We briefly review the Kapovich-Millson notion of Bending flows as an integrable system on the space of polygons in ${\mathbf{R}}^3$, its connection with a specific Gaudin XXX system, as well as the generalisation to $su(r),r>2$. Then we consider the quantisation problem of the set of Hamiltonians pertaining to the problem, quite naturally called Bending Hamiltonians, and prove that their commutativity is preserved at the quantum level.

7 pages, submitted to Czech. J. Phys

References in corpus (1)

• Quantum spectral curves, quantum integrable systems and the geometric Langlands correspondence

Cited by in corpus (1)

• Limits of Gaudin Systems: Classical and Quantum Cases