Real double coset spaces and their invariants

Details Real double coset spaces and their invariants Real double coset spaces and their invariants

2008-04-23

arxiv.org/abs/0804.3756v3

Mathematics

Representation Theory

18 pages, typos corrected

Scientific paper

Let G be a real form of a complex reductive group. Suppose that we are given involutions \sigma and \theta of G. Let H=G^\sigma denote the fixed group of \sigma and let K=G^\theta denote the fixed group of \theta. We are interested in calculating the double coset space H\backslash G/K. We use moment map and invariant theoretic techniques to calculate the double cosets, especially the ones that are closed. One salient point of our results is a stratification of a quotient of a compact torus over which the closed double cosets fiber as a collection of trivial bundles.

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