Equivariant fixed point formulae and Toeplitz operators under Hamiltonian torus actions

TL;DR

This paper develops asymptotic formulas for traces of equivariant Toeplitz operators under Hamiltonian torus actions, utilizing microlocal analysis of Szego kernels to advance understanding in geometric quantization.

Contribution

It introduces new asymptotic descriptions of equivariant Toeplitz operator traces under torus symmetries, employing microlocal analysis techniques.

Findings

Derived asymptotic formulas for traces along weight space rays.

Utilized microlocal analysis of Szego kernels for proofs.

Enhanced understanding of equivariant quantization processes.

Abstract

The main result of this paper is the description of asymptotics along rays in weight space of traces of equivariant Toeplitz operators composed with quantomorphisms for torus actions. The main ingredient in the proof is the microlocal analysis of the equivariant Szego kernels.