The Fourier transform of semi-simple coadjoint orbits
Let \(M\) be a closed coadjoint orbit of a real connected semisimple Lie group \(G\) and let \(F_M\) be its Fourier transform. The author computes the restriction of \(F_M\) to the Lie algebra \(\mathfrak k\) of a maximal compact subgroup \(K\) of \(G\). Using his technique of localization in equivariant cohomology (to be described in forthcoming papers in \textit{Compositio Mathematica} and \textit{Topology}), he extends previous results of Duflo, Heckman, Vergne, and Sengupta, which dealt with the elliptic and regular cases.
scientific article; zbMATH DE number 1278797
scientific article