Spin-quantization commutes with reduction

TL;DR

This paper proves that the principle of quantization commuting with reduction extends to the context of metaplectic correction, broadening the understanding of geometric quantization.

Contribution

It establishes that the Guillemin-Sternberg phenomenon holds when incorporating metaplectic correction, a significant extension of previous results.

Findings

Quantization commutes with reduction with metaplectic correction

Extension of Guillemin-Sternberg principle

Broader applicability in geometric quantization

Abstract

In this paper, we prove that the "quantization commutes with reduction" phenomenon of Guillemin-Sternberg applies in the context of the metaplectic correction.