arXiv subjects
Publications and source records attributed to Frederick Magata.
We present some results on reductions and the copolarity of isometric group actions, which we obtained in our thesis. We also describe a resolution construction for isometric actions with respect to a reduction and give examples.
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 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.
We prove an analogue of Weyl's Integration Formula for compact Lie groups in the context of polar actions. We also show how certain classical examples from the literature can be viewed as special cases of our result.