F-method for constructing equivariant differential operators

TL;DR

The paper introduces the F-method, an algebraic Fourier transform approach, to explicitly construct equivariant differential operators by solving differential equations, with applications in parabolic geometry and automorphic forms.

Contribution

It presents a novel algebraic Fourier transform technique (F-method) for constructing equivariant operators and analyzing branching laws in representation theory.

Findings

Explicit highest weight vectors obtained via the F-method.

Construction of natural equivariant operators in geometry and automorphic forms.

Demonstration of the method's applicability to concrete problems.

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.