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

Symmetry Integrability and Geometry-Methods and Applications

article

Yiannis Loizides¹ 

[1] Pennsylvania State University

关键词: symplectic geometry;    Hamiltonian G-spaces;    symplectic reduction;    geometric quantization;    quasi-polynomials;    stationary phase;   

DOI  :  10.3842/SIGMA.2019.090

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown