Convolution of invariant distributions: Proof of the Kashiwara-Vergne conjecture

Martin Andler (1) , Siddhartha Sahi (2) , Charles Torossian (3)

1 LMV - Laboratoire de Mathématiques de Versailles
2 Mathematics Department
3 IMJ - Institut de Mathématiques de Jussieu

Consider the Kontsevich $\star$-product on the symmetric algebra of a finite dimensional Lie algebra $\mathfrak g$, regarded as the algebra of distributions with support 0 on $\mathfrak g$. In this paper, we extend this $\star$-product to distributions satisfying an appropriate support condition. As a consequence, we prove a long standing conjecture of Kashiwara-Vergne on the convolution of germs of invariant distributions on the Lie group $G$.

Domaines: Algèbres quantiques [math.QA]; Théorie des représentations [math.RT]

Martin Andler, Siddhartha Sahi, Charles Torossian. Convolution of invariant distributions: Proof of the Kashiwara-Vergne conjecture. 2001. ⟨hal-00689880⟩