Applications de la bi-quantification \`a la th\'eorie de Lie

TL;DR

This survey explores bi-quantization applications in Lie theory, focusing on Duflo's conjecture, and introduces a new proof linking it to the Kashiwara-Vergne conjecture through polynomial deformation.

Contribution

It provides a new proof that the conjecture E=1 implies the Kashiwara-Vergne conjecture, using a non-geometric polynomial deformation approach.

Findings

Proves E=1 conjecture implies Kashiwara-Vergne conjecture

Connects bi-quantization with Duflo's conjecture in Lie theory

Introduces a novel polynomial deformation method

Abstract

This article is a survey about applications of bi-quantization theory in Lie theory. We focus on a conjecture of M. Duflo. Most of the applications are coming from our article with Alberto Cattaneo and some extensions are relating discussions with my student. The end of the article is completely new. We prove that the conjecture E=1 implies the Kashiwara-Vergne conjecture. Our deformation is non geometric but uses a polynomial deformation of the coefficients.