2000/07/26 by Victor Guillemin, Guillemin, Victor, Catalin Zara +1
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Representation Theory (math.RT) #Symplectic Geometry (math.SG) #math.RT #math.SG
paper · pdf · doi:10.48550/arxiv.math/0007165
19 pages
arxiv created 2000/07/26 · openalex publication_date 2000/07/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be an n-dimensional torus and τ a Hamiltonian action of G on a compact symplectic manifold, M. If M is pre-quantizable one can associate with τ a representation of G on a virtual vector space, Q(M), by \spin\CC-quantization. If M is a symplectic GKM manifold we will show that several well-known theorems about this ``quantum action'' of G: for example, the convexity theorem, the Kostant multiplicity theorem and the ``quantization commutes with reduction'' theorem for circle subgroups of G, are basically just theorems about G-actions on graphs.