Deformation quantization and invariant distributions

Abstract

In 1979, M. Kashiwara and M. Vergne formulated a conjecture on a Lie group G which implies that the Duflo isomorphism of Z(g) and S(g)^g extends to a natural module isomorphism between the spaces of germs of invariant distributions on G and g=Lie(G), respectively. They also proved their conjecture for G solvable. Using Kontsevich's deformation quantization we establish directly this result for distributions on any real Lie group G. In turn this gives a new proof of Duflo's result on the local solvability of bi-invariant differential operators on G.

6 pages, English + abridged French version (C. R. Acad. Sci. format). This is a short note, the expanded version will follow

Cited by in corpus (4)

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• Formality theorems for Hochschild complexes and their applications
• On triviality of the Kashiwara-Vergne problem for quadratic Lie algebras
• Poisson geometry and the Kashiwara-Vergne conjecture