Homogeneous Poisson Structures on Loop Spaces of Symmetric Spaces

Details Homogeneous Poisson Structures on Loop Spaces of Symmetric Spaces Homogeneous Poisson Structures on Loop Spaces of Symmetric Spaces

2008-01-21

arxiv.org/abs/0801.3277v4

SIGMA 4 (2008), 069, 33 pages

Mathematics

Symplectic Geometry

This is a contribution to the Special Issue on Kac-Moody Algebras and Applications, published in SIGMA (Symmetry, Integrabilit

Scientific paper

10.3842/SIGMA.2008.069

This paper is a sequel to [Caine A., Pickrell D., 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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