TY - BOOK
DB - /z-wcorg/
DP - http://worldcat.org
ID - 61309399
LA - English
T1 - Convexity properties of Hamiltonian group actions
AU - Guillemin, Victor,
AU - Sjamaar, Reyer,
PB - American Mathematical Society
CY - Providence, R.I.
Y1 - 2005///
SN - 0821839187 9780821839188
AB - "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.
ER -