Quantization of bending deformations of polygons in E 3 , hypergeometric integrals and the

The Hamiltonian potentials of the bending deformations of n-gons in E 3 studied in KM] and Kly] give rise to a Hamiltonian action of the Malcev Lie algebra P n of the pure braid group P n on the moduli space M r of n-gon linkages with the side-lengths r = (r 1 ; :::; r n) in E 3. If e 2 M r is a singular point we may linearize the vector elds in P n at e. This linearization yields a at connection r on the space C n of n distinct points on C. We show that the monodromy of r is the dual of a quotient of a specialized reduced Gassner representation.