A KK-theoretic perspective of quantization commutes with reduction

2020/11/01 by Rudy Rodsphon, Rodsphon, Rudy
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2011.00643

Abstract

We reframe Paradan-Vergne's approach to quantization commutes with reduction in KK-theory through a recent formalism introduced by Kasparov, focusing more especially the index theoretic parts that lead to their "Witten non-abelian localization formula". While our method uses the same ingredients as their's in spirit, interesting conceptual simplifications occur, and the relationship to the Ma-Tian-Zhang analytic approach becomes quite transparent.

Citations

• Geometric quantization and multiplicities of group representations

Related

• Geometric Quantization with Applications to Gromov-Witten Theory
• A K-Theoretic Note on Geometric Quantization
• An Introduction to Geometric Quantization and Witten's Quantum Invariant
• A Mathematical Introduction to Geometric Quantization
• A K-homological approach to the quantization commutes with reduction problem