The action of a compact Lie group, G, on a compact sympletic
manifold gives rise to some remarkable combinatorial invariants.
The simplest and most interesting of these is the moment polytopes,
a convex polyhedron which sits inside the dual of the Lie algebra
of G. One of the main goals of this monograph is to describe what
kinds of geometric information are encoded in this polytope. This
book is addressed to researchers and can be used as a semester
text.
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