Weylgruppe und Momentabbildung

Let G be a connected, reductive group defined over an alebraically closed field of characteristic zero. We assign to any G-variety X a finite cristallographic reflection group W_X by means of the moment map on the cotangent bundle. This generalizes the "little Weyl group" of a symmetric space.

We also determine the closure of the image of the moment map and the generic isotropy group of the action of G on the cotangent bundle. As a byproduct we determine the ideal of elements of U(g) which act trivially on X as a differential operator.

Appeared in: Inventiones Mathematicae 99 (1990) 1-23

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Remark: There is later paper devoted to the properties of the moment map. Many results are reproved there in a simpler way.

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Last updated: August 25, 2006