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- W1600822032 abstract "Let g be a simple Lie algebra, with corresponding connected Lie group G. Suppose g has a vector space splitting into a sum of subalgebras g = k + b, so that one can identify g' k + b*. By the Kostant-Symes involution theorem, the invariant functions on g*, when restricted to b, Poisson commute there, and in particular Poisson commute on co-adjoint orbits of B = exp b. Let Lg denote the loop algebra of smooth maps from S1 to g, whose Fourier series converge absolutely with respect to some weight function w. Using the Killing form of g, one can construct a canonical central extension Lg of Lg. For suitably chosen w, there exists a group LG corresponding to Lg, as well as Iwasawa decompositions at the algebra and group levels: Lg = k + a + ii, and LG = KAN. We apply the Kostant-Symes theorem to the splitting Lg = k + b, (where b = i + ii). Co-adjoint orbits in (Lg)* are parameterized by conjugacy classes in G, and so the class functions of G give rise to invariant functions on (Lg)'. When restricted to co-adjoint orbits of B = exp b, these functions Poisson commute. In this paper we realize the symmetric periodic Toda phase space associated with g, as a co-adjoint orbit of B, and show that the restricted invariant functions result in a completely integrable system on this orbit. Thesis Supervisor: Victor Guillemin Title: Professor" @default.
- W1600822032 created "2016-06-24" @default.
- W1600822032 creator A5011408960 @default.
- W1600822032 date "1995-01-01" @default.
- W1600822032 modified "2023-10-16" @default.
- W1600822032 title "A New Completely Integrable System on the Symmetric Periodic Toda Lattice Phase Space" @default.
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