Quasi-polynomials and the singular $[Q,R]=0$ theorem
Symplectic Geometry
2019-11-19 v2
Abstract
In this short note we revisit the `shift-desingularization' version of the 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.
Cite
@article{arxiv.1907.06113,
title = {Quasi-polynomials and the singular $[Q,R]=0$ theorem},
author = {Yiannis Loizides},
journal= {arXiv preprint arXiv:1907.06113},
year = {2019}
}