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The notion of polarity, as well as its use in the context of optimal reduction, can be seen as a particular case of a more general construction known generically as dual pair. This chapter reviews some of the definitions of the concept of dual pair encountered in the literature, the relations between them, and some of their applications in the context of momentum maps and reduction theory.
KeywordsSymplectic Manifold Poisson Structure Dual Pair Extension Property Poisson Manifold
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