Deformation quantization and invariant distributions

Martin Andler (1) , Alexander Dvorsky (2) , Siddhartha Sahi (2)

1 LMV - Laboratoire de Mathématiques de Versailles
2 Mathematics Department

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.

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

Martin Andler, Alexander Dvorsky, Siddhartha Sahi. Deformation quantization and invariant distributions. 1999. ⟨hal-00689888⟩