F-method for constructing equivariant differential operators

Abstract

Using an algebraic Fourier transform of operators, we develop a method (F-method) to obtain explicit highest weight vectors in the branching laws by differential equations. This article gives a brief explanation of the F-method and its applications to a concrete construction of some natural equivariant operators that arise in parabolic geometry and in automorphic forms.

8 pages (final version, Contemp Math. AMS)

References in corpus (1)

• Differential symmetry breaking operators. I-Genreal theory and F-method. II-Rankin-Cohen Operators for Symmetric Pairs

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• Symmetry breaking operators for real reductive groups of rank one
• Vector-valued covariant differential operators for the Möbius transformation
• Computation of Weighted Bergman Inner Products on Bounded Symmetric Domains and Restriction to Subgroups
• Conformal symmetry breaking on differential forms and some applications
• Computation of Weighted Bergman Inner Products on Bounded Symmetric Domains and Parseval-Plancherel-Type Formulas under Subgroups
• Conformally covariant differential symmetry breaking operators for a vector bundle of rank 3 over S^3
• Recent advances in branching problems of representations
• Computation of weighted Bergman inner products on bounded symmetric domains and restriction to subgroups II