Homogeneous Poisson structures on loop spaces of symmetric spaces

Doug Pickrell

doi:10.3842/SIGMA.2008.069

Homogeneous Poisson structures on loop spaces of symmetric spaces

Doug Pickrell

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

5 Scopus citations

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 language	English (US)
Article number	069
Journal	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume	4
DOIs	https://doi.org/10.3842/SIGMA.2008.069
State	Published - 2008

Keywords

Loop space
Poisson structure
Symmetric space
Toeplitz determinant

ASJC Scopus subject areas

Analysis
Mathematical Physics
Geometry and Topology

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10.3842/SIGMA.2008.069

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AB - 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.

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Homogeneous Poisson structures on loop spaces of symmetric spaces

Abstract

Keywords

ASJC Scopus subject areas

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