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 language | English (US) |
|---|---|
| Pages (from-to) | 371-390 |
| Number of pages | 20 |
| Journal | Annales Scientifiques de l'Ecole Normale Superieure |
| Volume | 35 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jan 1 2002 |
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ASJC Scopus subject areas
- Mathematics(all)
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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 journal › Article
}
TY - JOUR
T1 - Kontsevich quantization and invariant distributions on lie groups
AU - Andler, Martin
AU - Dvorsky, Alexander
AU - Sahi, Siddhartha
PY - 2002/1/1
Y1 - 2002/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0036318378&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0036318378&partnerID=8YFLogxK
U2 - 10.1016/S0012-9593(02)01093-5
DO - 10.1016/S0012-9593(02)01093-5
M3 - Article
AN - SCOPUS:0036318378
VL - 35
SP - 371
EP - 390
JO - Annales Scientifiques de l'Ecole Normale Superieure
JF - Annales Scientifiques de l'Ecole Normale Superieure
SN - 0012-9593
IS - 3
ER -