Duflo Isomorphism and Chern-Weil Theory

TL;DR

This paper explores the connection between the Duflo isomorphism and Chern-Weil theory through the distributional index of transversally elliptic operators on principal G-manifolds, linking algebraic and geometric aspects.

Contribution

It provides a novel interpretation of the Duflo isomorphism in terms of Chern-Weil forms via the distributional index of transversally elliptic operators.

Findings

Established a link between the distributional index and Duflo isomorphism.

Connected algebraic isomorphisms with geometric Chern-Weil forms.

Proposed a new perspective on index theory in the context of principal G-manifolds.

Abstract

We explain how the distributional index of a transversally elliptic operator on a principal G-manifold P that is obtained by lifting a Dirac operator on P/G can serve as a link between the Duflo isomorphism and Chern-Weil forms.