A general Weyl-type Integration Formula for Isometric Group Actions

Details A general Weyl-type Integration Formula for Isometric Group Actions A general Weyl-type Integration Formula for Isometric Group Actions

2009-01-16

arxiv.org/abs/0901.2515v1

Mathematics

Differential Geometry

14 pages, based on the authors docotral thesis

Scientific paper

We show that integration over a $G$-manifold $M$ can be reduced to integration over a minimal section $\Sigma$ with respect to an induced weighted measure and integration over a homogeneous space $G/N$. We relate our formula to integration formulae for polar actions and calculate some weight functions. In case of a compact Lie group acting on itself via conjugation, we obtain a classical result of Hermann Weyl. Our formula allows to view almost arbitrary isometric group actions as generalized random matrix ensembles. We also establish a reductive decomposition of Killing fields with respect to a minimal section.

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