
Journal of Lie Theory 18 (2008), No. 1, 093123 Copyright Heldermann Verlag 2008 Transvection and Differential Invariants of Parametrized Curves Gloria Marí Beffa Mathematics Department, University of Wisconsin, Madison, WI 53706, U.S.A. maribeff@math.wisc.edu Jan A. Sanders Mathematics Department, Vrije Universiteit, 1081 HV Amsterdam, Netherlands jansa@cs.vu.nl We describe an sl_{2} representation in the space of differential invariants of parametrized curves in homogeneous spaces. The representation is described by three operators, one of them being the total derivative D. We use this representation to find a basis for the space of differential invariants of curves in a complement of the image of D, and so generated by transvection. These are natural representatives of first cohomology classes in the invariant bicomplex. We describe algorithms to find these basis and study most wellknown geometries. Keywords: Transvectant, differential invariants, curves, affine manifold, symmetric manifold. MSC: 13A50, 53A55 [ Fulltextpdf (288 KB)] for subscribers only. 