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Convexity properties of Hamiltonian group actions

Author: Victor Guillemin; Reyer Sjamaar
Publisher: Providence, R.I. : American Mathematical Society, ©2005.
Series: CRM monograph series, v. 26.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:
"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
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Additional Physical Format: Online version:
Guillemin, Victor, 1937-
Convexity properties of Hamiltonian group actions.
Providence, R.I. : American Mathematical Society, c2005
(OCoLC)625304811
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Victor Guillemin; Reyer Sjamaar
ISBN: 0821839187 9780821839188
OCLC Number: 61309399
Description: iv, 82 p. : ill. ; 27 cm.
Contents: Ch. 1. The convexity theorem for Hamiltonian G-spaces --
Ch. 2. A constructive proof of the non-abelian convexity theorem --
Ch. 3. Some elementary examples of the convexity theorem --
Ch. 4. Kahler potentials and convexity --
Ch. 5. Applications of the convexity theorem.
Series Title: CRM monograph series, v. 26.
Responsibility: Victor Guillemin, Reyer Sjamaar.
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Abstract:

Describes convexity properties of moment mappings in symplectic geometry. This book reviews various infinite-dimensional manifestations of moment convexity, such as the Kostant type theorems for  Read more...

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schema:reviewBody""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, and an elementary Morse-theoretic argument deriving the Klyachko inequalities and some of their generalizations."
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