2 6 Fe b 20 01 Integrable systems associated with the Bruhat Poisson structures
نویسنده
چکیده
The purpose of this note is to give a simple description of a complete family of functions in involution on certain hermitian symmetric spaces. This family obtained via bi-hamiltonian approach using the Bruhat Poisson structure is especially simple for projective spaces, where the formulas in terms of the moment map coordinates are presented. Relations with the Toda lattice are outlined (we plan on giving more details in a future paper).
منابع مشابه
Integrable Systems on Flag Manifold and
We construct integrable models on ag manifold by using the symplectic structure explicitly given in the Bruhat coordinatization of ag manifold. They are non-commutative integrable and some of the conserved quantities are given by the Casimir invariants. We quantize the systems using the coherent state path integral technique and nd the exact expression for the propagator for some special cases....
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The standard Poisson structure on the rectangular matrix variety M m,n (C) is investigated, via the orbits of symplectic leaves under the action of the maximal torus T ⊂ GL m+n (C). These orbits, finite in number, are shown to be smooth irreducible locally closed subvarieties of M m,n (C), isomorphic to intersections of dual Schubert cells in the full flag variety of GL m+n (C). Three different...
متن کاملPoisson Structures on Complex Flag Manifolds Associated with Real Forms
For a complex semisimple Lie group G and a real form G0 we define a Poisson structure on the variety of Borel subgroups of G with the property that all G0-orbits in X as well as all Bruhat cells (for a suitable choice of a Borel subgroup of G) are Poisson submanifolds. In particular, we show that every non-empty intersection of a G0-orbit and a Bruhat cell is a regular Poisson manifold, and we ...
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We investigate ergodic theory of Poisson suspensions. In the process, we establish close connections between finite and infinite measure preserving ergodic theory. Poisson suspensions thus provide a new approach to infinite measure ergodic theory. Fields investigated here are mixing properties, spectral theory, joinings. We also compare Poisson suspensions to the apparently similar looking Gaus...
متن کاملFe b 20 04 Poisson structures compatible with the canonical metric of IR 3
In this Note, we will characterize the Poisson structures compatible with the canonical metric of IR. We will also give some relevant examples of such structures. The notion of compatibility between a Poisson structure and a Riemannian metric used in this Note was introduced and studied by the author in [1], [2], [3].
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تاریخ انتشار 2001