By Victor Guillemin

The motion of a compact Lie staff, G, on a compact sympletic manifold offers upward push to a few awesome combinatorial invariants. the easiest and finest of those is the instant polytopes, a convex polyhedron which sits contained in the twin of the Lie algebra of G. one of many major ambitions of this monograph is to explain what forms of geometric details are encoded during this polytope. This publication is addressed to researchers and will be used as a semester text.

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