Kontsevich quantization and invariant distributions on lie groups

Martin Andler, Alexander Dvorsky, Siddhartha Sahi

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

We study Kontsevich's deformation quantization for the dual of a finite-dimensional real Lie algebra (or superalgebra) g. In this case the Kontsevich -product defines a new convolution on S(g), regarded as the space of distributions supported at 0 ∈ g. For p ∈ S(g), we show that the convolution operator f → p f 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 G. This implies local solvability of bi-invariant differential operators on a Lie supergroup. In the special case of Lie groups, we get a new proof Duflo's theorem.

Original languageEnglish (US)
Pages (from-to)371-390
Number of pages20
JournalAnnales Scientifiques de l'Ecole Normale Superieure
Volume35
Issue number3
DOIs
StatePublished - Jan 1 2002

ASJC Scopus subject areas

  • Mathematics(all)

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