Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Completeness of determinantal Hamiltonian flows on the matrix affine
  Poisson space   The matrix affine Poisson space (M_{m,n}, pi_{m,n}) is the space of complex
rectangular matrices equipped with a canonical quadratic Poisson structure
which in the square case m=n reduces to the standard Poisson structure on
GL_n(C). We prove that the Hamiltonian flows of all minors are complete. As a
corollary we obtain that all Kogan-Zelevinsky integrable systems on M_{n,n} are
complete and thus induce (analytic) Hamiltonian actions of C^{n(n-1)/2} on
(M_{n,n}, pi_{n,n}) (as well as on GL_n(C) and on SL_n(C)).
  We define Gelfand-Zeitlin integrable systems on (M_{n,n}, pi_{n,n}) from
chains of Poisson projections and prove that their flows are also complete.
This is an analog for the quadratic Poisson structure pi_{n,n} of the recent
result of Kostant and Wallach [KW] that the flows of the complexified classical
Gelfand-Zeitlin integrable systems are complete.

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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: hep-th