Quantization of affinely-rigid bodies with degenerate dimension

Discussed is Schrödinger quantization of the classical object the configuration space of which is given by the manifold of affine injections from the “material space” into the “physical space” of higher dimension. The special stress is laid on the physical 2- and 3-dimensional situation and on the dynamical models isotropic both in space and material. Basing on the Peter-Weyl theorem we show how to reduce effectively the problem from 6 to 2 degrees of freedom, where as yet no further reduction or separation is found.