We briefly review the Kapovich-Millson notion of bending flows as an integrable system on the space of polygons inR 3, its connection with a specific GaudinXXX system, as well as the generalization to su(r),r>2. Then we consider the quantization 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.
Key wordsLax matrices XXX Gaudin models quantum integrable systems
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