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A general Weyl-type integration formula for isometric group actions

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Abstract

We show that integration over a G-manifold M can be reduced to integration over a minimal section Σ with respect to an induced weighted measure and integration over a homogeneous space G/N. We relate our formula to integration formulæ for polar actions and calculate some weight functions. In the case of a compact Lie group acting on itself via conjugation, we obtain a classical result of Hermann Weyl.

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Authors and Affiliations

  1. Department of Mathematics, University of Münster, Einsteinstr. 62, 48149, Münster, Germany

    Frederick Magata

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  1. Frederick Magata
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Correspondence to Frederick Magata.

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Dedicated to my “academic family” in Münster

The author received financial support by the DFG-Schwerpunkt 1145 “Globale Differentialgeometrie” and the University of Münster. This paper is based on parts of the authors doctoral thesis [M2].

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Magata, F. A general Weyl-type integration formula for isometric group actions. Transformation Groups 15, 184–200 (2010). https://doi.org/10.1007/s00031-010-9076-7

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  • DOI: https://doi.org/10.1007/s00031-010-9076-7

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