Kashiwara-Vergne-Rouviere methods for symmetric spaces

TL;DR

This paper extends the Campbell-Hausdorff formula to symmetric spaces using Kontsevich's deformation, recovering Rouviere's results on invariant distributions for specific types of symmetric spaces.

Contribution

It introduces a novel application of Kontsevich's deformation to symmetric spaces, generalizing Rouviere's convolution results.

Findings

Recovered Rouviere's results for solvable symmetric spaces

Extended methods to 'very symmetric spaces'

Connected deformation quantization with symmetric space analysis

Abstract

This article follows our previous work on Campbell-Hausdorff formula. We study the case of symmetric spaces. We recover, by using a Kontsevich's deformation of the Baker-Campbell-Hausdorff formula, Rouviere's results on the convolution of invariant distributions, for solvable symmetric spaces and "very symmetric spaces".