This article is cited in 1 paper

Quasi-Polynomials and the Singular $[Q,R]=0$ Theorem

Yiannis Loizides

Pennsylvania State University, USA

Abstract: 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, quasi-polynomials, stationary phase.

MSC: 53D20; 53D50

Received: July 16, 2019; in final form November 13, 2019; Published online November 18, 2019

Language: English

DOI: 10.3842/SIGMA.2019.090

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ArXiv: 1907.06113