The isotropy representation for homogeneous Siegel domains

Joseph Eugene D’Atri, Josef Dorfmeister and Yan Da Zhao

Vol. 120 (1985), No. 2, 295–326

DOI: 10.2140/pjm.1985.120.295

Abstract

This paper gives several new characterizations of symmetric domains among the class of homogeneous Siegel domains. These characterizations involve the commutativity of the algebra of invariant differential operators, the transitivity of the action of the isotropy group on the Šilov boundary, and the representation of the almost complex structure by the infinitesimal isotropy action, respectively.

Mathematical Subject Classification 2000

Primary: 32M05

Secondary: 32M15, 53C30

Milestones

Received: 15 October 1983

Published: 1 December 1985