Kontsevich quantization and invariant distributions on Lie groups
Abstract
We study Kontsevich's deformation quantization for the dual of a finitedimensional real Lie algebra (or superalgebra) g. In this case the Kontsevich starproduct defines a new convolution on S(g), regarded as the space of distributions supported at 0 in g. For p in S(g), we show that the convolution operator f>f*p is a differential operator with analytic germ. We use this fact to prove a conjecture of Kashiwara and Vergne on invariant distributions on a Lie group. This yields a new proof of Duflo's result on local solvability of biinvariant differential operators on a Lie group. Moreover, this new proof extends to Lie supergroups.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 1999
 arXiv:
 arXiv:math/9910104
 Bibcode:
 1999math.....10104A
 Keywords:

 Quantum Algebra;
 Differential Geometry;
 Representation Theory
 EPrint:
 22 pages, LaTeX. This is an expanded version of math.QA/9905065