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

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4 Citations (Scopus)

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 2006

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Symmetric Spaces
Invariant Measure
Denote
Complexification
Stationary Phase
Fixed Point Set
Poisson Structure
Compact Lie Group
Involution
Probability Measure
Geodesic
Triangular
Fourier transform
Decompose

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

The diagonal distribution for the invariant measure of a unitary type symmetric space. / Pickrell, Douglas M.

In: Transformation Groups, Vol. 11, No. 4, 12.2006, p. 705-724.

Research output: Contribution to journalArticle

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