Cotangent Bundles as Coadjoint Orbits and Asymptotic Character Formulas

TL;DR

This paper explores the geometric quantization of cotangent bundles viewed as coadjoint orbits of an infinite-dimensional Lie group, and develops asymptotic character formulas using the tangent groupoid.

Contribution

It demonstrates how cotangent bundles can be realized as coadjoint orbits and introduces new asymptotic character formulas via the tangent groupoid.

Findings

Realization of cotangent bundles as coadjoint orbits of an infinite-dimensional Lie group

Development of two asymptotic character formulas using the tangent groupoid

Connection between geometric quantization and Kirillov's orbit method

Abstract

The present article presents geometric quantization on cotangent bundles as a special instance of Kirillov's orbit method. To this end, the cotangent bundle is realized as a coadjoint orbit of an infinite-dimensional Lie group constructed from the diffeomorphism group. We also develop two asymptotic character formulas by employing the tangent groupoid.