The diagonal distribution for the invariant measure of a unitary type symmetric space

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

Let Θ denote an involution for a simply connected compact Lie group U let K denote the fixed point set and let μ denote the U-invariant probability measure on U/K. Consider the geodesic embedding φ :U/K → U:u → uu -Θ of Cartan. In this paper we compute the Fourier transform of the diagonal distribution for φ*μ relative to a compatible triangular decomposition of G the complexification of U. This boils down to a Duistermaat-Heckman exact stationary phase calculation involving a Poisson structure on the dual symmetric space G0/K discovered by Evens and Lu.

Original languageEnglish (US)
Pages (from-to)705-724
Number of pages20
JournalTransformation Groups
Volume11
Issue number4
DOIs
StatePublished - Dec 1 2006

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

Fingerprint Dive into the research topics of 'The diagonal distribution for the invariant measure of a unitary type symmetric space'. Together they form a unique fingerprint.

  • Cite this