Kontsevich quantization and invariant distributions on lie groups

Martin Andler, Alexander Dvorsky, Siddhartha Sahi

Research output: Contribution to journalArticle

12 Citations (Scopus)

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

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Invariant Distribution
Quantization
Local Solvability
Invariant Differential Operators
Deformation Quantization
Convolution Operator
Lie Superalgebra
Differential operator
Convolution
Lie Algebra
Imply
Theorem

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Kontsevich quantization and invariant distributions on lie groups. / Andler, Martin; Dvorsky, Alexander; Sahi, Siddhartha.

In: Annales Scientifiques de l'Ecole Normale Superieure, Vol. 35, No. 3, 01.01.2002, p. 371-390.

Research output: Contribution to journalArticle

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