2011/10/05 by Michel Duflo, Duflo, Michel, Michèle Vergne +1
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.1110.0987
openalex publication_date 2011/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a connected reductive real Lie group, and H a compact connected subgroup. Harish-Chandra associates to a regular coadjoint admissible orbit M of G some unitary representations of G. Using the character formula for these representations, we show that the multiplicities of the restriction to H can be computed, under a suitable properness assumption, in terms of the fibers of the restriction map from M to the dual of the Lie algebra of H. In particular, this gives an alternate proof of a result of Paradan.