Bulletin of the Australian Mathematical Society

Table of Contents - 1990 - Volume 42, Issue 02  

Research Article

Orbital decompositions of representations of non-simply connected nilpotent groups

Ronald L. Lipsmana1

a1 Department of Mathematics, University of Maryland College Park, MD 20742, United States of America

Abstract

An orbital integral formula is proven for the direct integral decomposition of an induced representation of a connected nilpotent Lie group. Previous work required simple connectivity. An explicit description of the spectral measure and spectral multiplicity function is derived in terms of orbital parameters. It is also proven that connected (but not necessarily simply connected) exponential solvable symmetric spaces are multiplicity free. Finally, the qualitative properties of the spectral multiplicity function are examined via several illuminating examples.

(Received November 02 1989)