Homogeneous Poisson structures on symmetric spaces

Arlo Caine, Douglas M Pickrell

Research output: Contribution to journalArticle

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Abstract

We calculate, in a relatively explicit way, the Hamiltonian systems that arise from the Evens-Lu construction of homogeneous Poisson structures on both compact- and noncompact-type symmetric spaces. A corollary is that the Hamiltonian system arising in the noncompact case is isomorphic to the generic Hamiltonian system arising in the compact case. In the group case, these systems are also isomorphic to those arising from the Bruhat-Poisson structure on the flag space, and hence, by results of Lu, can be completely factored.

Original languageEnglish (US)
Pages (from-to)98-140
Number of pages43
JournalInternational Mathematics Research Notices
Volume2009
Issue number1
DOIs
StatePublished - 2009

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Homogeneous Structure
Poisson Structure
Symmetric Spaces
Hamiltonian Systems
Isomorphic
Corollary
Calculate

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Homogeneous Poisson structures on symmetric spaces. / Caine, Arlo; Pickrell, Douglas M.

In: International Mathematics Research Notices, Vol. 2009, No. 1, 2009, p. 98-140.

Research output: Contribution to journalArticle

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