Representation of compact Lie groups and quantization by deformation

In: Bulletin de la Classe des Sciences de l'Académie Royale de Sciences, des Lettres et des Beaux-Arts de Belgique, Band 74, Heft 1, S. 123-141

Abstract

We realise the *-representation program for compact semi simple Lie groups, using a Kodaira's map and Berezin's symbols. We study the Fourier transform it induces. We show that injectivity of Kodaira's map selects the data of geometric quantization. In this case an inverse of Kodaira's map is given by a moment map. This relates our construction to existing ones.