The Hua operators on homogeneous line bundle on Bounded Symmetric Domains of Tube Type

TL;DR

This paper characterizes the image of the Poisson transform on certain principal series representations of bounded symmetric domains of tube type using covariant differential operators on homogeneous line bundles.

Contribution

It provides a new characterization of the Poisson transform's image via covariant differential operators on homogeneous line bundles on tube type domains.

Findings

Image of Poisson transform characterized by covariant differential operators.

Connection established between principal series representations and differential operators.

Provides tools for analysis on bounded symmetric domains of tube type.

Abstract

Let D be a bounded symmetric domain of tube type . We show that the image of the Poisson transform on the degenerate principal series representation attached to the Shilov boundary of D is characterized by a covariant differential operator on a homogeneous line bundle on D.