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Weylgruppe und Momentabbildung. (Weyl group and moment map). (German) Zbl 0726.20031
Let a connected, reductive algebraic group G defined over an algebraically closed field of characteristic zero act on an algebraic variety X. A construction is given, which assigns, to X, by means of the moment map of the cotangent bundle a finite cristallographic reflection group \(W_ X\). This group generalizes the little Weyl group of a symmetric space; one has \(W_ X=1\) iff X is horospherical, i.e. \(X=G.X^ U\), U being a maximal unipotent subgroup of G. The group \(W_ X\) is related to the equivariant compactification theory of X. The closure of the image of the moment map and the generic stabilizer of the action of G on the cotangent bundle are determined, as well as the ideal of elements of U(Lie G) which act trivially on X.
Reviewer: V.L.Popov (Moskva)

MSC:
20G15 Linear algebraic groups over arbitrary fields
20H15 Other geometric groups, including crystallographic groups
14L30 Group actions on varieties or schemes (quotients)
20G05 Representation theory for linear algebraic groups
14L35 Classical groups (algebro-geometric aspects)
20G10 Cohomology theory for linear algebraic groups
57S25 Groups acting on specific manifolds
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