This article is cited in 1 paper

Invariant Ordering on the Simply Connected Covering of the Shilov Boundary of a Symmetric Domain

A. L. Konstantinov

M. V. Lomonosov Moscow State University

Abstract: The Shilov boundary of a symmetric domain $D=G/K$ of tube type has the form $G/P$, where $P$ is a maximal parabolic subgroup of the group $G$. We prove that the simply connected covering of the Shilov boundary possesses a unique (up to inversion) invariant ordering, which is induced by the continuous invariant ordering on the simply connected covering of $G$ and can readily be described in terms of the corresponding Jordan algebra.

Keywords: invariant cone, invariant ordering, Lie semigroup.

UDC: 512.816.4

Received: 07.09.2006

DOI: 10.4213/faa2888

 English version: Functional Analysis and Its Applications, 2008, 42:1, 28–32

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