Homogeneous Poisson structures on loop spaces of symmetric spaces

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5 Citations (Scopus)

Abstract

This paper is a sequel to [Caine A., Pickrell D., Int. Math. Res. Not., to appear, arXiv:0710.4484], where we studied the Hamiltonian systems which arise from the Evens-Lu construction of homogeneous Poisson structures on both compact and noncompact type symmetric spaces. In this paper we consider loop space analogues. Many of the results extend in a relatively routine way to the loop space setting, but new issues emerge. The main point of this paper is to spell out the meaning of the results, especially in the SU(2) case. Applications include integral formulas and factorizations for Toeplitz determinants.

Original languageEnglish (US)
Article number069
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume4
DOIs
StatePublished - 2008

Fingerprint

Homogeneous Structure
Loop Space
Poisson Structure
Symmetric Spaces
Toeplitz Determinant
Integral Formula
Hamiltonian Systems
Factorization
Analogue
Meaning

Keywords

  • Loop space
  • Poisson structure
  • Symmetric space
  • Toeplitz determinant

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology
  • Mathematical Physics

Cite this

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