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Convexity properties of Hamiltonian group actions

著者: Victor Guillemin; Reyer Sjamaar
出版商: Providence, R.I. : American Mathematical Society, ©2005.
丛书: CRM monograph series, v. 26.
版本/格式:   图书 : 英语查看所有的版本和格式
数据库:WorldCat
提要:
"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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附加的形体格式: Online version:
Guillemin, Victor, 1937-
Convexity properties of Hamiltonian group actions.
Providence, R.I. : American Mathematical Society, c2005
(OCoLC)625304811
材料类型: 互联网资源
文件类型: 书, 互联网资源
所有的著者/提供者: Victor Guillemin; Reyer Sjamaar
ISBN: 0821839187 9780821839188
OCLC号码: 61309399
描述: iv, 82 p. : ill. ; 27 cm.
内容: 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.
丛书名: CRM monograph series, v. 26.
责任: Victor Guillemin, Reyer Sjamaar.
更多信息:

摘要:

"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.

It reviews various infinite-dimensional manifestations of moment convexity, such as the Kostant type theorems for orbits of a loop group (due to Atiyah and Pressley) or a symplectomorphism group (due to Bloch, Flaschka and Ratiu). Finally, it gives an account of a new convexity theorem for moment map images of orbits of a Borel subgroup of a complex reductive group acing on a Kahler manifold, based on potential-theoretic methods in several complex variables."--BOOK JACKET.

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