Convexity properties of Hamiltonian group actions / Victor Guillemin, Reyer Sjamaar.

Format:

Book

Author/Creator:

Guillemin, Victor, 1937- author.

Sjamaar, Reyer, 1961- author.

Series:

CRM monograph series ; Volume 26.

CRM Monograph Series ; Volume 26

Language:

English

Subjects (All):

Hamiltonian systems.

Convex domains.

Matrices.

Convex functions.

Convexity spaces.

Physical Description:

1 online resource (90 pages) : illustrations.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2012.

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 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 su This volume is recommended for independent study and is suitable for graduate students and researchers interested in symplectic geometry, algebraic geometry, and geometric combinatorics.

Notes:

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-1772-3