Families of equivariant differential operators and anti de Sitter spaces

TL;DR

This paper constructs and characterizes a sequence of differential operators that intertwine spherical principal series representations on anti de Sitter space boundaries, linking algebraic and geometric aspects.

Contribution

It introduces a new family of equivariant differential operators for anti de Sitter spaces and establishes their algebraic and geometric properties.

Findings

Existence and uniqueness of the differential operators

Connection to homomorphisms of generalized Verma modules

Relation to eigenfunction asymptotics on anti de Sitter spaces

Abstract

We prove existence and uniqueness of a sequence of differential intertwining operators for spherical principal series representations, which are realized on boundaries of anti de Sitter spaces. Algebraically, these operators correspond to homomorphisms of generalized Verma modules. We relate these families to the asymptotics of eigenfunctions on anti de Sitter spaces.