Quantization of Bending Deformations of Polygons In E3, Hypergeometric Integrals and the Gassner Representation
نویسندگان
چکیده
The Hamiltonian potentials of the bending deformations of n-gons in E3 studied in [KM] and [Kly] give rise to a Hamiltonian action of the Malcev Lie algebra Pn of the pure braid group Pn on the moduli space Mr of n-gon linkages with the side-lengths r = (r1, . . . , rn) in E3. If e ∈ Mr is a singular point we may linearize the vector fields inPn at e. This linearization yields a flat connection∇ on the space C∗ of n distinct points on C. We show that the monodromy of∇ is the dual of a quotient of a specialized reduced Gassner representation.
منابع مشابه
Quantization of bending deformations of polygons in E, hypergeometric integrals and the Gassner representation
The Hamiltonian potentials of the bending deformations of n-gons in E3 studied in [KM] and [Kly] give rise to a Hamiltonian action of the Malcev Lie algebra Pn of the pure braid group Pn on the moduli space Mr of n-gon linkages with the side-lengths r = (r1, ..., rn) in E 3. If e ∈ Mr is a singular point we may linearize the vector fields in Pn at e. This linearization yields a flat connection ...
متن کاملQuantization 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 connecti...
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