Convexity Properties of Hamiltonian Group Actionsby Victor Guillemin, Reyer Sjamaar
Pub. Date: 11/28/2005
Publisher: American Mathematical Society
This is a monograph on convexity properties of moment mappings in symplectic geometry. The fundamental result in this subject is the Kirwan convexity theorem, which describes the image of a moment map in terms of linear inequalities. This theorem bears a close relationship to perplexing old puzzles from linear algebra, such as the Horn problem on sums of Hermitian matrices, on which considerable progress has been made in recent years following a breakthrough by Klyachko. The book presents a simple local model for the moment polytope, valid in the generic" case.
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