메뉴 건너뛰기




Volumn 90, Issue 2, 1997, Pages 261-377

Méthode des orbites de kirillov-duflo et représentations minimales des groupes simples sur un corps local de caractéristique nulle

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0000906876     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-97-09009-8     Document Type: Article
Times cited : (48)

References (59)
  • 1
    • 13844289709 scopus 로고
    • Représentations des groupes de Lie résolubles
    • Dunod, Paris
    • P. Bernât et al., Représentations des groupes de Lie résolubles, Monographies Soc. Math. France 4, Dunod, Paris, 1972.
    • (1972) Monographies Soc. Math. France , vol.4
    • Bernât, P.1
  • 2
    • 0002971194 scopus 로고
    • All reductive groups are tame
    • I. N. Bernstein, All reductive groups are tame, Funct. Anal. Appl. 8 (1974), 91-93.
    • (1974) Funct. Anal. Appl. , vol.8 , pp. 91-93
    • Bernstein, I.N.1
  • 4
    • 51249187393 scopus 로고
    • Compléments à l’article: “Groupes réductifs,”
    • A. Borel et J. Tits, Compléments à l’article: “Groupes réductifs,” Inst. Hautes Études Sci. Publ. Math. 41 (1972), 253-276.
    • (1972) Inst. Hautes Études Sci. Publ. Math. , vol.41 , pp. 253-276
    • Tits, A.B.E.J.1
  • 5
    • 4243726809 scopus 로고
    • Eléments de mathématique, F asc. 34, Groupes et algèbres de Lie, Chapitres 4, 5 et 6
    • Hermann, Paris
    • N. Bourbaki, Eléments de mathématique, F asc. 34, Groupes et algèbres de Lie, Chapitres 4, 5 et 6, Actualités Sci. Indust. 1337, Hermann, Paris, 1968.
    • (1968) Actualités Sci. Indust , vol.1337
    • Bourbaki, N.1
  • 6
    • 0028351872 scopus 로고
    • Minimal representations of Es, Et, and Eg and the generalized Capelli identity
    • R. Brylinski et B. Kostant, Minimal representations of Es, Et, and Eg and the generalized Capelli identity, Proc. Nat. Acad. Sci. U.S.A. (1994), 2469-2472.
    • (1994) Proc. Nat. Acad. Sci. U.S.A , pp. 2469-2472
    • Kostant, R.B.E.B.1
  • 7
    • 0028201022 scopus 로고
    • Minimal representations, geometric quantization, and unitarity
    • R. Brylinski et B. Kostant, Minimal representations, geometric quantization, and unitarity, Proc. Nat. Acad. Sci. U.S.A. (1994), 6026-6029.
    • (1994) Proc. Nat. Acad. Sci. U.S.A , pp. 6026-6029
    • Kostant, R.B.E.B.1
  • 8
    • 0010062945 scopus 로고
    • Differential operators on conical Lagrangian manifolds dans Lie Theory and Geometry
    • Honor of B. Kostant, éd. J.-L. Brylinski et al, Birkhâuser, Boston
    • R. Brylinski et B. Kostant, “Differential operators on conical Lagrangian manifolds” dans Lie Theory and Geometry: In Honor of B. Kostant, éd. J.-L. Brylinski et al., Progr. Math. 123, Birkhâuser, Boston, 1994, 65-96.
    • (1994) Progr. Math , vol.123 , pp. 65-96
    • Kostant, R.B.E.B.1
  • 9
    • 0002591368 scopus 로고
    • Lagrangian models of minimal representations of E^, Eq and E% dans Functional Analysis on the Eve of the 21st Century
    • éd. S. Gindikin et al, Birkhâuser, Boston
    • R. Brylinski et B. Kostant, “Lagrangian models of minimal representations of E^, Eq and E%” dans Functional Analysis on the Eve of the 21st Century, éd. S. Gindikin et al., Progr. Math. 131, Birkhâuser, Boston, 1995, 13-63.
    • (1995) Progr. Math , vol.131 , pp. 13-63
    • Kostant, R.B.E.B.1
  • 10
    • 0039821026 scopus 로고
    • On central extensions of rational points of algebraic groups
    • V. V. Deodhar, On central extensions of rational points of algebraic groups, Amer. J. Math. 100 (1978), 303-386.
    • (1978) Amer. J. Math , vol.100 , pp. 303-386
    • Deodhar, V.V.1
  • 11
    • 33646053237 scopus 로고
    • Algèbres enveloppantes
    • Gauthier-Villars, Paris
    • J. Dixmier, Algèbres enveloppantes, Cahiers Sci. 37, Gauthier-Villars, Paris, 1974.
    • (1974) Cahiers Sci , vol.37
    • Dixmier, J.1
  • 12
    • 34250224162 scopus 로고
    • Théorie de Mackey pour les groupes de Lie algébriques
    • M. Duflo, Théorie de Mackey pour les groupes de Lie algébriques, Acta Math. 149 (1982), 153-213.
    • (1982) Acta Math , vol.149 , pp. 153-213
    • Duflo, M.1
  • 13
    • 0005667503 scopus 로고
    • On the Plancherel formula for almost algebraic real Lie groups dans Lie Group
    • éd. R. Herb et al, Springer-Verlag, Berlin
    • M. Duflo, “On the Plancherel formula for almost algebraic real Lie groups” dans Lie Group Representations, III, éd. R. Herb et al., Lecture Notes in Math. 1077, Springer-Verlag, Berlin, 1984, 101-165.
    • (1984) Lecture Notes in Math , vol.1077 , pp. 101-165
    • Duflo, M.1    Representations, I.2
  • 14
    • 51249171910 scopus 로고
    • Savin, Explicit realization of a metaplectic representation
    • Y. Flicker, D. Kazhdan, et G. Savin, Explicit realization of a metaplectic representation, J. Anal. Math. 55 (1990), 17-39.
    • (1990) J. Anal. Math , vol.55 , pp. 17-39
    • Flicker, Y.1    Kazhdan, D.2    Et, G.3
  • 15
    • 0039139521 scopus 로고
    • Constructions of the Weil representations of certain Lie algebras, Funct. Anal
    • A. B. Goncharov, Constructions of the Weil representations of certain Lie algebras, Funct. Anal. Appl. 16 (1982), 133-135.
    • (1982) Appl , vol.16 , pp. 133-135
    • Goncharov, A.B.1
  • 16
    • 0038511792 scopus 로고
    • A distinguished family of unitary representations for the exceptional groups of real rank = 4 dans Lie Theory and Geometry
    • Honor of B. Kostant, éd. J.-L. Brylinski et al, Birkhâuser, Boston
    • B. H. Gross N. Wallach, “A distinguished family of unitary representations for the exceptional groups of real rank = 4” dans Lie Theory and Geometry: In Honor of B. Kostant, éd. J.-L. Brylinski et al., Progr. Math. 123, Birkhâuser, Boston, 1994, 289-304.
    • (1994) Progr. Math , vol.123 , pp. 289-304
    • Gross, B.H.1    Wallach, N.2
  • 17
    • 0001057066 scopus 로고
    • dans Lie Theories and Their Applications (Proc. Ann. Sent. Canad. Math. Congr., Queen's Univ., Kingston, Ont., 1977), Queen’s Papers in Pure and Appl. Math. 48, Queen’s Univ., Kingston, Ont
    • Harish-Chandra H, “Admissible invariant distributions on reductive p-adic groups” dans Lie Theories and Their Applications (Proc. Ann. Sent. Canad. Math. Congr., Queen's Univ., Kingston, Ont., 1977), Queen’s Papers in Pure and Appl. Math. 48, Queen’s Univ., Kingston, Ont., 1978, 281-347.
    • (1978) Admissible Invariant Distributions on Reductive P-Adic Groups , pp. 281-347
    • Harish-Chandra, H.1
  • 19
    • 0010064908 scopus 로고
    • The geometry of nilpotent coadjoint orbits of convex type in hermitean Lie algebras
    • J. Hilgert, K.-H. Neeb et B. Ørsted, The geometry of nilpotent coadjoint orbits of convex type in hermitean Lie algebras, J. Lie Theory 4 (1994), 185-235.
    • (1994) J. Lie Theory , vol.4 , pp. 185-235
    • Hilgert, J.1    Ørsted, K.-H.N.E.B.2
  • 20
    • 25444505898 scopus 로고    scopus 로고
    • Conal Heisenberg algebras and associated Hilbert spaces
    • J. Hilgert, K.-H. Neeb et B. Ørsted, Conal Heisenberg algebras and associated Hilbert spaces, J. Reine Angew. Math. 474 (1996), 67-112.
    • (1996) J. Reine Angew. Math. , vol.474 , pp. 67-112
    • Hilgert, J.1    Ørsted, K.-H.N.E.B.2
  • 21
    • 0010794879 scopus 로고    scopus 로고
    • Unitary highest weight representations via the orbit method, I, the scalar case: Representations of Lie groups, Lie algebras and their quantum analogues
    • J. Hilgert, K.-H. Neeb et B. Ørsted, Unitary highest weight representations via the orbit method, I, the scalar case: Representations of Lie groups, Lie algebras and their quantum analogues, Acta Appl. Math. 44 (1996), 151-184.
    • (1996) Acta Appl. Math , vol.44 , pp. 151-184
    • Hilgert, J.1    Neeb Et, K.-H.2    Ørsted, B.3
  • 22
    • 84972494158 scopus 로고
    • Topics in harmonic analysis on solvable algebraic groups
    • R. Howe, Topics in harmonic analysis on solvable algebraic groups. Pacific J. Math. 73 (1977), 383-435.
    • (1977) Pacific J. Math , vol.73 , pp. 383-435
    • Howe, R.1
  • 23
    • 0009300472 scopus 로고
    • Small unitary representations of classical groups dans Group Representations, Ergodic Theory, Operator Algebras, and Mathematical Physics
    • éd. C. C. Moore, Springer-Verlag, New York
    • R. Howe, “Small unitary representations of classical groups” dans Group Representations, Ergodic Theory, Operator Algebras, and Mathematical Physics, éd. C. C. Moore, Math. Sci. Res. Inst. Publ. 6, Springer-Verlag, New York, 1987, 121-150.
    • (1987) Math. Sci. Res. Inst. Publ , vol.6 , pp. 121-150
    • Howe, R.1
  • 24
    • 0002797638 scopus 로고
    • The minimal orbit in a simple Lie algebra and its associated maximal ideal
    • A. Joseph, The minimal orbit in a simple Lie algebra and its associated maximal ideal, Ann. Sci. École Norm. Sup. (4) 9 (1976), 1-29.
    • (1976) Ann. Sci. École Norm. Sup , vol.9 , Issue.4 , pp. 1-29
    • Joseph, A.1
  • 25
    • 0003375422 scopus 로고
    • The minimal representation of D4 dans Operator Algebras, Unitary Representations, Enveloping Algebras, and Invariant Theory
    • éd. A. Connes et al, Birkhâuser, Boston
    • D. Kazhdan, “The minimal representation of D4” dans Operator Algebras, Unitary Representations, Enveloping Algebras, and Invariant Theory, éd. A. Connes et al., Progr. Math. 92, Birkhâuser, Boston, 1990, 125-158.
    • (1990) Progr. Math , vol.92 , pp. 125-158
    • Kazhdan, D.1
  • 27
    • 0000269229 scopus 로고
    • The smallest representation of simply laced groups dans Festschrift in Honor of 1.1. Piatetski-Shapiro on the Occasion of His Sixtieth Birthday
    • Weizmann, Jerusalem
    • D. Kazhdan et G. Savin, “The smallest representation of simply laced groups” dans Festschrift in Honor of 1.1. Piatetski-Shapiro on the Occasion of His Sixtieth Birthday, Part /, Israel Math. Conf. Proc. 2 Weizmann, Jerusalem, 1990, 209-223.
    • (1990) Part /, Israel Math. Conf. Proc , vol.2 , pp. 209-223
    • Savin, D.K.E.G.1
  • 28
    • 0001991328 scopus 로고
    • Unitary representations of nilpotent Lie groups (In Russian)
    • A. A. Kirillov, Unitary representations of nilpotent Lie groups (in Russian), Uspehi Mat. Nauk 17 (1962), 57-110.
    • (1962) Uspehi Mat. Nauk , vol.17 , pp. 57-110
    • Kirillov, A.A.1
  • 29
    • 38249029067 scopus 로고
    • The minimal nilpotent orbit, the Joseph ideal, and differential operators
    • T. Levasseur, S. P. Smith, et J. T. Stafford, The minimal nilpotent orbit, the Joseph ideal, and differential operators, J. Algebra 116 (1988), 480-501.
    • (1988) J. Algebra , vol.116 , pp. 480-501
    • Levasseur, T.1    Smith, S.P.2    Stafford, E.J.T.3
  • 30
    • 30244439513 scopus 로고
    • Indices de Maslov et représentation de Weil dans Three lectures on the Representations of Nilpotent and Solvable Groups
    • Paris
    • G. Lion, “Indices de Maslov et représentation de Weil” dans Three lectures on the Representations of Nilpotent and Solvable Groups, Publ. Math. Univ. Paris VII 2, Univ. Paris VII, Paris, 1978, 45-79.
    • (1978) Publ. Math. Univ. Paris VII 2, Univ. Paris VII , pp. 45-79
    • Lion, G.1
  • 31
    • 0000855579 scopus 로고
    • Extension des représentations de groupes unipotents p-adiques: Caculs dobstructions” dans Noncommutative Harmonie Analysis and Lie Groups (Marseille, 1980)
    • éd. J. Carmona et M. Vergne, Springer-Verlag, Berlin
    • G. Lion et P. Perrin, “Extension des représentations de groupes unipotents p-adiques: Caculs d’obstructions” dans Noncommutative Harmonie Analysis and Lie Groups (Marseille, 1980), éd. J. Carmona et M. Vergne, Lecture Notes in Math. 880, Springer-Verlag, Berlin, 1981, 337-356.
    • (1981) Lecture Notes in Math , vol.880 , pp. 337-356
    • Perrin, G.L.E.P.1
  • 32
    • 0003342718 scopus 로고
    • The Weil Representation, Maslov Index and Theta Series
    • Birkhäuser, Boston
    • G. Lion et M. Vergne, The Weil Representation, Maslov Index and Theta Series, Progr. Math. 6, Birkhäuser, Boston, 1980.
    • (1980) Progr. Math , vol.6
    • Vergne, G.L.E.M.1
  • 33
    • 0002807628 scopus 로고
    • Sur les sous-groupes arithmétiques des groupes semi-simples déployés
    • H. Matsumoto, Sur les sous-groupes arithmétiques des groupes semi-simples déployés, Ann. Sei. École Norm. Sup. (4) 2 (1969), 1-62.
    • (1969) Ann. Sei. École Norm. Sup , vol.2 , Issue.4 , pp. 1-62
    • Matsumoto, H.1
  • 34
    • 0000410176 scopus 로고
    • Modèles de Whittaker dégénérés pour les groupes, p-adiques
    • Moeglin et J.-L. Waldspurger, Modèles de Whittaker dégénérés pour les groupes, p-adiques, Math. Z. 196 (1987), 427-452.
    • (1987) Math. Z , vol.196 , pp. 427-452
    • Waldspurger, M.E.J.-L.1
  • 35
    • 84968514037 scopus 로고
    • Extensions and low dimensional cohomology theory of locally compact groups
    • II, 113 (1964), 64-86
    • C. C. Moore, Extensions and low dimensional cohomology theory of locally compact groups. I, Trans. Amer. Math. Soc. 113 (1964), 40-63; II, 113 (1964), 64-86.
    • (1964) I, Trans. Amer. Math. Soc , vol.113 , pp. 40-63
    • Moore, C.C.1
  • 36
    • 0013297129 scopus 로고
    • Decomposition of unitary representations defined by discrete subgroups of nilpotent groups
    • C. C. Moore, Decomposition of unitary representations defined by discrete subgroups of nilpotent groups, Ann. of Math. (2) 82 (1965), 146-182.
    • (1965) Ann. Of Math , vol.82 , Issue.2 , pp. 146-182
    • Moore, C.C.1
  • 37
    • 0001189904 scopus 로고
    • Group extensions of p-adic and adelic linear groups
    • C. C. Moore, Group extensions of p-adic and adelic linear groups, Inst. Hautes Etudes Sei. Publ. Math. 35 (1968), 157-222.
    • (1968) Inst. Hautes Etudes Sei. Publ. Math , vol.35 , pp. 157-222
    • Moore, C.C.1
  • 38
    • 84968482231 scopus 로고
    • Group extensions and cohomology for locally compact groups, III
    • IV, 221 (1976), 35-58
    • C. C. Moore, Group extensions and cohomology for locally compact groups, III, Trans. Amer. Math. Soc. 221 (1976), 1-33; IV, 221 (1976), 35-58.
    • (1976) Trans. Amer. Math. Soc , vol.221 , pp. 1-33
    • Moore, C.C.1
  • 39
    • 0009035998 scopus 로고
    • Représentations de Schrödinger, indice de Maslov et groupe métaplectique dans N oncommutative Harmonie Analysis and Lie Groups (Marseille, 1980)
    • éd. J. Carmona et M. Vergne, Springer-Verlag, Berlin
    • P. Perrin, “Représentations de Schrödinger, indice de Maslov et groupe métaplectique” dans N oncommutative Harmonie Analysis and Lie Groups (Marseille, 1980), éd. J. Carmona et M. Vergne, Lecture Notes in Math. 880, Springer-Verlag, Berlin, 1981, 370-407.
    • (1981) Lecture Notes in Math , vol.880 , pp. 370-407
    • Perrin, P.1
  • 40
    • 0039013134 scopus 로고
    • On C00-vectors and intertwining bilinear forms for representations of Lie groups
    • 00-vectors and intertwining bilinear forms for representations of Lie groups, J. Funct. Anal. 9 (1972), 87-120.
    • (1972) J. Funct. Anal , vol.9 , pp. 87-120
    • Poulsen, N.1
  • 41
    • 0003236669 scopus 로고
    • Topological central extensions of semisimple groups over local fields, I
    • II, 119 (1984), 203-268. -, Topological central extensions ofSLi(D), Invent. Math. 92 (1988), 645-689
    • G. Prasad et M. S. Raghunathan, Topological central extensions of semisimple groups over local fields, I, Ann. of Math. (2) 119 (1984), 143-201; II, 119 (1984), 203-268. -, Topological central extensions ofSLi(D), Invent. Math. 92 (1988), 645-689.
    • (1984) Ann. Of Math , vol.119 , Issue.2 , pp. 143-201
    • Prasad, G.1    Raghunathan, M.S.2
  • 43
    • 0039157452 scopus 로고
    • Unitary representations of solvable Lie groups
    • L. Pukanszky, Unitary representations of solvable Lie groups, Ann. Sei. École Norm. Sup. (4) 4 (1971), 457-608.
    • (1971) Ann. Sei. École Norm. Sup , vol.4 , Issue.4 , pp. 457-608
    • Pukanszky, L.1
  • 44
    • 0030138855 scopus 로고    scopus 로고
    • Une représentation unipotente associée à Vorbite minimale: Le cas de SOo(4,3)
    • H. Sabourin, Une représentation unipotente associée à Vorbite minimale: le cas de SOo(4,3), J. Funct. Anal. 137 (1996), 394-465.
    • (1996) J. Funct. Anal , vol.137 , pp. 394-465
    • Sabourin, H.1
  • 45
    • 34249772836 scopus 로고
    • Dual pair G/ x PGL2, [where] G/ is the automorphism group of the Jordan algebra
    • G. Savin, Dual pair G/ x PGL2, [where] G/ is the automorphism group of the Jordan algebra /, Invent. Math. 118 (1994), 141-160.
    • (1994) Invent. Math , vol.118 , pp. 141-160
    • Savin, G.1
  • 46
    • 0039229114 scopus 로고
    • Fundamental groups of semisimple symmetric spaces, dans Representations of Lie Groups, Kyoto, Hiroshima, 1986
    • Academic Press, Boston
    • J. Sekiguchi, “Fundamental groups of semisimple symmetric spaces,” dans Representations of Lie Groups, Kyoto, Hiroshima, 1986, Adv. Stud. Pure Math. 14, Academic Press, Boston, 1988, 519-529.
    • (1988) Adv. Stud. Pure Math , vol.14 , pp. 519-529
    • Sekiguchi, J.1
  • 47
    • 85037198511 scopus 로고
    • Cours d’arithmétique, SUP: “Le Mathématicien” 2
    • Paris
    • J-P. Serre, Cours d’arithmétique, SUP: “Le Mathématicien” 2, Presses Universitaires de France, Paris, 1970.
    • (1970) Presses Universitaires De France
    • Serre, J.-P.1
  • 49
    • 0040657308 scopus 로고
    • Corps locaux, 2d éd
    • Hermann, Paris
    • J-P. Serre, Corps locaux, 2d éd., Publ. Univ. Nancago 8, Hermann, Paris, 1968.
    • (1968) Publ. Univ. Nancago , vol.8
    • Serre, J.-P.1
  • 50
    • 84951885157 scopus 로고
    • Linear symmetries of free boson fields
    • D. Shale, Linear symmetries of free boson fields, Trans. Amer. Math. Soc. 103 (1962), 149 167.
    • (1962) Trans. Amer. Math. Soc , vol.103 , Issue.149 , pp. 167
    • Shale, D.1
  • 51
    • 85037247645 scopus 로고
    • Théorie de Mackey pour les groupes adéliques, Astérisque
    • Montrouge
    • M.-H. Sliman, Théorie de Mackey pour les groupes adéliques, Astérisque 115, Soc. Math. France, Montrouge, 1984.
    • (1984) Soc. Math. France , vol.115
    • Sliman, M.-H.1
  • 52
    • 84968518235 scopus 로고
    • Gelfand-Kirillov dimension of rings of formal differential operators on affine varieties
    • S. P. Smith, Gelfand-Kirillov dimension of rings of formal differential operators on affine varieties, Proc. Amer. Math. Soc. 90 (1984), 1-8.
    • (1984) Proc. Amer. Math. Soc , vol.90 , pp. 1-8
    • Smith, S.P.1
  • 54
    • 0005377530 scopus 로고
    • Groupes de Whitehead de groupes algébriques simples sur un corps (D'après V. P. Platonov et al.), Séminaire N. Bourbaki, 29e année (1976/77)
    • Springer-Verlag, Berlin
    • J. Trrs, Groupes de Whitehead de groupes algébriques simples sur un corps (d'après V. P. Platonov et al.), Séminaire N. Bourbaki, 29e année (1976/77), Lecture Notes in Math. 677, Springer-Verlag, Berlin, 1978, 218-236.
    • (1978) Lecture Notes in Math , vol.677 , pp. 218-236
    • Trrs, J.1
  • 55
    • 0011434749 scopus 로고
    • Quantification géométrique, opérateurs d'entrelacement et représentations unitaires de S∼L3(ÏÏL)
    • 3(ÏÏL), Acta Math. 150 (1983), 153-242.
    • (1983) Acta Math , vol.150 , pp. 153-242
    • Torasso, P.1
  • 56
    • 0001183081 scopus 로고
    • Associated varieties and unipotent representations dans Harmonie Analysis on Reductive Groups (Brunswick, Maine, 1989)
    • éd. W. Barker et P. Sally, Birkhâuser, Boston
    • D. Vogan, “Associated varieties and unipotent representations” dans Harmonie Analysis on Reductive Groups (Brunswick, Maine, 1989), éd. W. Barker et P. Sally, Progr. Math. 101, Birkhâuser, Boston, 1991, 315-388.
    • (1991) Progr. Math , vol.101 , pp. 315-388
    • Vogan, D.1
  • 57
    • 0001406110 scopus 로고
    • The unitary dual of G2
    • D. Vogan, The unitary dual of G2, Invent. Math. 116 (1994), 677-791.
    • (1994) Invent. Math , vol.116 , pp. 677-791
    • Vogan, D.1
  • 58
    • 34250594733 scopus 로고
    • Sur certains groupes d’opérateurs unitaires
    • A. Weil, Sur certains groupes d’opérateurs unitaires, Acta. Math. Ill (1964), 143-211.
    • (1964) Acta. Math. Ill , pp. 143-211
    • Weil, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.