Deformation quantization and invariant distributions
Quantum Algebra
2009-10-31 v2 Differential Geometry
Representation Theory
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.
Cite
@article{arxiv.math/9905065,
title = {Deformation quantization and invariant distributions},
author = {Martin Andler and Alexander Dvorsky and Siddhartha Sahi},
journal= {arXiv preprint arXiv:math/9905065},
year = {2009}
}
Comments
6 pages, English + abridged French version (C. R. Acad. Sci. format). This is a short note, the expanded version will follow