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Homogeneous Poisson Structures on Loop Spaces of Symmetric Spaces
Symmetry, integrability and geometry: methods and applications, Tome 4 (2008) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: Poisson structure; loop space; symmetric space; Toeplitz determinant. 
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Doug Pickrell. Homogeneous Poisson Structures on Loop Spaces of Symmetric Spaces. Symmetry, integrability and geometry: methods and applications, Tome 4 (2008). http://geodesic.mathdoc.fr/item/SIGMA_2008_4_a68/

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