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- W2082305885 abstract "First the definition of the infinite dimensional Grassmannian over the Hilbert space LR2[0,1] = E ⊕ U is given, where the polarization is according to the even and odd functions. We then prove that the normal space Nq(M(p)) at the point q ϵ M(e), where M(e) is the isospectral set to the even point e, belongs to the Grassmannian over LR2[0, 1]. Since an element of the normal space depends not only on its base point but also on a parameter x ϵ [0, 1], we first fix x, and for arbitrary q ϵ M(e) we derive the group action on the Grassmannian. The determinant bundle and the tau function are constructed over the Grassmannian whereas in contrast to the usual constructions regularized determinants are involved. For fixed elements of the isospectral set and the variation of the parameter x the second group which acts on the Grassmannian is derived. It is then shown how a unified construction for both group acting on the Grassmannian has to be carried out by comparing it to the Fock bundle construction of 3 + 1 dimensional Dirac-Yang-Mills theories." @default.
- W2082305885 created "2016-06-24" @default.
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- W2082305885 date "1996-03-01" @default.
- W2082305885 modified "2023-10-16" @default.
- W2082305885 title "Geometry and analysis on isospectral sets. II. Grassmannian, determinant bundle and the tau function, asymptotic case" @default.
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- W2082305885 doi "https://doi.org/10.1016/0393-0440(95)00011-9" @default.
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