Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 4 (2008), 069, 33 pages      arXiv:0801.3277
Contribution to the Special Issue on Kac-Moody Algebras and Applications

Homogeneous Poisson Structures on Loop Spaces of Symmetric Spaces

Doug Pickrell
Department of Mathematics, University of Arizona, Tucson, AZ, 85721, USA

Received June 14, 2008, in final form September 27, 2008; Published online October 07, 2008

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.

Key words: Poisson structure; loop space; symmetric space; Toeplitz determinant.

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