F-method for symmetry breaking operators
arXiv:1303.3541 · doi:10.1016/j.difgeo.2013.10.003
Abstract
We provide some insights in the study of branching problems of reductive groups, and a method of investigations into symmetry breaking operators. First, we give geometric criteria for finiteness property of linearly independent continuous (respectively, differential) operators that intertwine two induced representations of reductive Lie groups and their reductive subgroups. Second, we extend the F-method known for local operators to non-local operators. We then illustrate the idea by concrete examples in conformal geometry, and explain how the F-method works for detailed analysis of symmetry breaking operators, e.g., finding functional equations and explicit residue formulae of regular symmetry breaking operators with meromorphic parameters.
to appear in Differential Geom. Appl
References in corpus (4)
- Finite multiplicity theorems for induction and restriction
- Symmetry breaking for representations of rank one orthogonal groups
- F-method for constructing equivariant differential operators
- Differential symmetry breaking operators. I-Genreal theory and F-method. II-Rankin-Cohen Operators for Symmetric Pairs
Cited by in corpus (14)
- Symmetry breaking for representations of rank one orthogonal groups
- A program for branching problems in the representation theory of real reductive groups
- Symmetry breaking for representations of rank one orthogonal groups II
- Classification of finite-multiplicity symmetric pairs
- Shintani functions, real spherical manifolds, and symmetry breaking operators
- Estimates for the restriction of automorphic forms on hyperbolic manifolds to compact geodesic cycles
- Residue formula for regular symmetry breaking operators
- Symmetry breaking differential operators, the source operator and Rodrigues formulæ
- Inversion of Rankin-Cohen operators via Holographic Transform
- Vector-valued covariant differential operators for the Möbius transformation
- Conformally covariant differential symmetry breaking operators for a vector bundle of rank 3 over S^3
- Residue Family Operators on Spinors and Spectral Theory of Dirac operator on Poincaré-Einstein Spaces
- Symmetry Breaking Differential Operators for Tensor Products of Spinorial Representations
- Recent advances in branching problems of representations