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Opérateurs différentiels bi-invariants sur un groupe de Lie. (French) Zbl 0353.22009


MSC:

22E30 Analysis on real and complex Lie groups
58J99 Partial differential equations on manifolds; differential operators
35E05 Fundamental solutions to PDEs and systems of PDEs with constant coefficients
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References:

[1] P. BERNAT , N. CONZE et coll., Représentations des groupes de Lie résolubles , Dunod, Paris, 1972 . MR 56 #3183 | Zbl 0248.22012 · Zbl 0248.22012
[2] A. BOREL , Linear Algebraic Groups , Benjamin, New York, 1969 . MR 40 #4273 | Zbl 0186.33201 · Zbl 0186.33201
[3] J. DIXMIER , Algèbres enveloppantes , Gauthier-Villars, Paris, 1974 . MR 58 #16803a | Zbl 0308.17007 · Zbl 0308.17007
[4] J. DIXMIER , M. DUFLO et M. VERGNE , Sur la représentation coadjointe d’une algèbre de Lie (Compositio Mathematica, vol. 29, 1974 , p. 309-323). Numdam | MR 51 #630 | Zbl 0296.17009 · Zbl 0296.17009
[5] M. DUFLO , Caractères des groupes et des algèbres de Lie résolubles (Ann. scient. Éc. Norm. Sup., t. 3, 1970 , p. 23-74). Numdam | MR 42 #4672 | Zbl 0223.22016 · Zbl 0223.22016
[6] M. DUFLO , Construction of Primitive Ideals in an Enveloping Algebra (In Lie Groups and their Representations, Adam Hilger Ltd., London, 1975 ). MR 53 #3045 | Zbl 0313.17005 · Zbl 0313.17005
[7] M. DUFLO et M. RAÏS , Sur l’analyse harmonique sur les groupes de Lie résolubles (Ann. scient. Éc. Norm. Sup., vol. 9, 1976 , p. 107-144). Numdam | MR 55 #8254 | Zbl 0324.43011 · Zbl 0324.43011
[8] S. HELGASON , Solvability of Invariant Differential Operators on Homogeneous Manifolds (In Differential Operators on Manifold, C.I.M.E., cremoneze, Rome, 1975 ). MR 58 #29860 · Zbl 0309.53049
[9] A. A. KIRILLOV , The Characters of Unitary Representations of Lie Groups (Functional Analysis and its Applications, vol. 2, 1968 , p. 40-55). MR 38 #4615 | Zbl 0174.45001 · Zbl 0174.45001
[10] A. A. KIRILLOV , Characters of Unitary Representations of Lie Groups . Reduction Theorems (Functiona Analysis and its Applications, vol. 3, 1969 , p. 36-47). MR 40 #1538 | Zbl 0194.33901 · Zbl 0194.33901
[11] M. RAÏS , Solutions élémentaires des opérateurs différentiels bi-invariants sur un groupe de Lie nilpotent (C.R. Acad. Sc. Paris, t. 273, série A, 1971 , p. 495-498). MR 44 #6908 | Zbl 0236.46047 · Zbl 0236.46047
[12] G. WARNER , Harmonic Analysis on Semi-simple Lie Groups II , Springer-Verlag, Berlin, 1972 . Zbl 0265.22021 · Zbl 0265.22021
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