Matrix coefficients and coadjoint orbits of compact Lie groups

Abstract

Abstract. Let G be a compact Lie group. We use Weyl functional calculus (Anderson, 1969) and symplectic convexity theorems to determine the support and singular support of the operator-valued Fourier transform of the product of the j-function and the pull-back of an arbitrary unitary irreducible representation of G to the Lie algebra, strengthening and generalizing the results of Cazzaniga, 1992. We obtain as a consequence a new demonstration of the Kirillov correspondence for compact Lie groups.