Quantization of q-Hamiltonian SU(2)-spaces

TL;DR

This paper develops a method to quantize q-Hamiltonian SU(2)-spaces using twisted K-homology and proves a 'quantization commutes with reduction' theorem, connecting to Verlinde formulas for flat bundles.

Contribution

It introduces a new approach to quantization via twisted K-homology and establishes a key theorem linking quantization and reduction in this context.

Findings

Quantization of q-Hamiltonian SU(2)-spaces defined via twisted K-homology.

Proof of 'quantization commutes with reduction' theorem in this setting.

Derivation of Verlinde formulas for flat bundles through localization in twisted K-homology.

Abstract

We explain how to define the quantization of q-Hamiltonian SU(2)-spaces as push-forwards in twisted K-homology, and prove a `quantization commutes with reduction' theorem for this setting. As applications, we show how the Verlinde formulas for flat SU(2) or SO(3) bundles are obtained by localization in twisted K-homology.