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

Doug Pickrell

doi:10.1016/j.jfa.2005.09.008

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

Doug Pickrell

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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 language	English (US)
Pages (from-to)	321-363
Number of pages	43
Journal	Journal of Functional Analysis
Volume	234
Issue number	2
DOIs	https://doi.org/10.1016/j.jfa.2005.09.008
State	Published - May 15 2006

Keywords

Invariant measure
Loop groups
Loop spaces
Wiener measure

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2005.09.008

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title = "An invariant measure for the loop space of a simply connected compact symmetric space",

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.",

keywords = "Invariant measure, Loop groups, Loop spaces, Wiener measure",

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N2 - 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.

AB - 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.

KW - Invariant measure

KW - Loop groups

KW - Loop spaces

KW - Wiener measure

UR - https://www.scopus.com/pages/publications/33645860843

UR - https://www.scopus.com/pages/publications/33645860843#tab=citedBy

U2 - 10.1016/j.jfa.2005.09.008

DO - 10.1016/j.jfa.2005.09.008

M3 - Article

AN - SCOPUS:33645860843

SN - 0022-1236

VL - 234

SP - 321

EP - 363

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 2

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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