Kirillov’s orbit method: The case of discrete series representations

2017/09/04 by Paul-Emile Paradan
Mathematics · #(g,K)-module #Adjoint representation #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Lie group #Orbit (dynamics) #Reductive group #Representation (politics) #Representation theory #Series (stratigraphy) #math.RT #math.SG

paper · pdf · doi:10.1215/00127094-2019-0059

published as Duke Math. J. 168, no. 16 (2019), 3103-3134

arxiv created 2017/09/04 · openalex created_date 2017/09/15 · openalex publication_date 2019/10/24 · arxiv updated 2019/12/19 · openalex updated_date 2026/08/05

Abstract

Let π be a discrete series representation of a real reductive Lie group G', and let G be a reductive subgroup of G'. In this paper, we give a geometric expression of the G-multiplicities in π|G when the representation π is G-admissible.

Citations

• Symplectic Surgery and the Spinc–Dirac Operator
• Non-abelian convexity by symplectic cuts
• Geometric quantization and multiplicities of group representations
• Heat Kernels and Dirac Operators
• A proof of Blattner's conjecture
• L 2 -Cohomology and the Discrete Series
• Equivariant Dirac operators and differentiable geometric invariant theory