An invariant measure for the loop space of a simply connected compact symmetric space

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Let X denote a simply connected compact Riemannian symmetric space, U the universal covering of the identity component of the group of automorphisms of X, and LU the loop group of U. In this paper we prove the existence (and conjecture the uniqueness) of an LU-invariant probability measure on a distributional completion of the loop space of X.

Original languageEnglish (US)
Pages (from-to)321-363
Number of pages43
JournalJournal of Functional Analysis
Volume234
Issue number2
DOIs
StatePublished - May 15 2006

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Riemannian Symmetric Space
Loop Groups
Loop Space
Compact Space
Symmetric Spaces
Invariant Measure
Probability Measure
Completion
Automorphisms
Covering
Uniqueness
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Keywords

  • Invariant measure
  • Loop groups
  • Loop spaces
  • Wiener measure

ASJC Scopus subject areas

  • Analysis

Cite this

An invariant measure for the loop space of a simply connected compact symmetric space. / Pickrell, Douglas M.

In: Journal of Functional Analysis, Vol. 234, No. 2, 15.05.2006, p. 321-363.

Research output: Contribution to journalArticle

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