Convexity properties of Hamiltonian group actions
By: Victor Guillemin, Reyer Sjamaar.
Contributors: Sjamaar, Reyer, 1961-
Series: CRM monograph series,; v. 26
Publisher: Americam Mathematical Society
Published: 2005
Place of publication: Providence, R.I
Language: eng
Number of pages: 82
Subjects: Hamiltonian systems.; Convex domains.; Matrices.; Convex functions.; Convexity spaces.
Description: "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."--Jacket.
Notes: Includes bibliographical references.