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Quasi-Polynomials and the Singular $[Q,R]=0$ Theorem
Symmetry, integrability and geometry: methods and applications, Tome 15 (2019) Cet article a éte moissonné depuis la source Math-Net.Ru

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In this short note we revisit the ‘shift-desingularization’ version of the $[Q,R]=0$ theorem for possibly singular symplectic quotients. We take as starting point an elegant proof due to Szenes–Vergne of the quasi-polynomial behavior of the multiplicity as a function of the tensor power of the prequantum line bundle. We use the Berline–Vergne index formula and the stationary phase expansion to compute the quasi-polynomial, adapting an early approach of Meinrenken.
Keywords: symplectic geometry, Hamiltonian $G$-spaces, symplectic reduction, geometric quantization, stationary phase.
Mots-clés : quasi-polynomials 
@article{SIGMA_2019_15_a89,
     author = {Yiannis Loizides},
     title = {Quasi-Polynomials and the {Singular} $[Q,R]=0$ {Theorem}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2019},
     volume = {15},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a89/}
}
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Yiannis Loizides. Quasi-Polynomials and the Singular $[Q,R]=0$ Theorem. Symmetry, integrability and geometry: methods and applications, Tome 15 (2019). http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a89/

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