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

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.