@article{CM_1992__82_2_189_0, author = {Matumoto, Hisayosi}, title = {$C^{-\infty }$-Whittaker vectors corresponding to a principal nilpotent orbit of a real reductive linear Lie group, and wave front sets}, journal = {Compositio Mathematica}, volume = {84}, year = {1992}, pages = {189-244}, zbl = {0797.22005}, language = {en}, url = {http://dml.mathdoc.fr/item/CM_1992__82_2_189_0} }
Matumoto, Hisayosi. $C^{-\infty }$-Whittaker vectors corresponding to a principal nilpotent orbit of a real reductive linear Lie group, and wave front sets. Compositio Mathematica, Tome 84 (1992) pp. 189-244. http://gdmltest.u-ga.fr/item/CM_1992__82_2_189_0/
[1] The local structure of characters, J. Funct. Anal. 37 (1980), 27-55. | MR 576644 | Zbl 0436.22011
and :[2] Primitive ideals and orbital integrals in complex classical groups, Math. Ann. 259 (1982), 153-199. | MR 656661 | Zbl 0489.22010
and :[3] Primitive ideals and orbital integrals in complex exceptional groups, J. Algebra 80 (1983), 350-382. | MR 691809 | Zbl 0513.22009
and :[4] Unipotent representations of complex semisimple Lie groups, Ann. of Math. 121 (1985), 41-110. | MR 782556 | Zbl 0582.22007
and :[5] Weyl group representations and nilpotent orbits, in: P.C. Trombi (ed.), Representation Theory of Reductive Groups, Progress in Mathematics Vol. 40, 21-33, Birkhäuser, Boston-Basel- Stuttgart, 1983. | MR 733804 | Zbl 0537.22013
and :[6] Tensor product of finite and infinite dimensional representations of semisimple Lie algebras, Compositio Math. 41 (1980), 245-285. | Numdam | MR 581584 | Zbl 0445.17006
and :[7] Automorphic Forms on GL(3, R), Lecture Notes in Mathematics No. 1083, Springer-Verlag, Berlin-Heidelberg-New York, 1984. | MR 765698 | Zbl 0543.22005
:[8] A letter to Harish-Chandra, November 30, 1982.
:[9] Canonical extensions of Harish-Chandra modules to representations of G, Can. J. Math. 41 (1989), 385-438. | MR 1013462 | Zbl 0702.22016
:[10] Primitive ideals and representations, J. of Algebra 101 (1986), 497-515. | MR 847174 | Zbl 0598.17006
:[11] Horospherical functions on symmetric spaces, Canadian Mathematical Society Conference Proceedings 1 (1981), 125-133. | Zbl 0545.43008
:[12] Whittaker vectors and conical vectors, J. Funct. Anal. 39 (1980), 199-279. | MR 597811 | Zbl 0475.22010
and :[13] Whittaker models for semisimple Lie groups, Japan J. Math. 5 (1979), 349-401. | MR 614828 | Zbl 0506.22016
:[14] Whittaker functions on semisimple Lie groups, Hiroshima Math. J. 13 (1982), 259-293. | MR 665496 | Zbl 0524.43005
:[15] A proof of Blattner's conjecture, Invent. Math. 31 (1975), 129-154. | MR 396855 | Zbl 0319.22012
and :[16] Fourier integral operators I, Acta Math. 127 (1971), 79-183. | MR 388463 | Zbl 0212.46601
:[17] Wave front sets of representations of Lie groups, in: Automorphic Forms, Representation Theory, and Arithmetic, Bombay, 1981. | MR 633659 | Zbl 0494.22010
:[18] Fonction de Whittaker associées aux groupes de Chevalley, Bull. Soc. Math. France 95 (1967), 243-309. | Numdam | MR 271275 | Zbl 0155.05901
:[19] Automorphic Form on GL(2), Lecture Notes in Mathematics, No. 114, Springer-Verlag, Berlin-Heidelberg-New York, 1970. | MR 401654 | Zbl 0236.12010
and :[20] Goldie rank in the enveloping algebra of a semisimple Lie algebra I, J. Algebra 65 (1980), 269-283. | MR 585721 | Zbl 0441.17004
:[21] Goldie rank in the enveloping algebra of a semisimple Lie algebra II, J. Algebra 65 (1980), 284-306. | MR 585721 | Zbl 0441.17004
:[22] On the associated variety of a primitive ideal, J. Algebra 93 (1985), 509-523. | MR 786766 | Zbl 0594.17009
:[23] The invariant holonomic system on a semisimple Lie group, in: Algebraic Analysis (papers dedicated to Professor Mikio Sato on the occasion of his sixtieth birthday) Vol. 1, pp. 277-286, Academic Press, San Diego, 1988. | MR 992461 | Zbl 0704.22008
:[24] Second-microlocalization and asymptotic expansions, in: Lecture Notes in Physics No. 126, pp. 21-76, Springer-Verlag, Berlin-Heidelberg -New York, 1980. | MR 579740 | Zbl 0458.46027
and :[25] Functions on the Shilov boundary of the generalized half plane, in: Non-Commutative Harmonic Analysis, Lecture Notes in Mathematics No. 728, Springer-Verlag, Berlin-Heidelberg- New York, 1979. | MR 548329 | Zbl 0416.22006
and :[26] K-types and the singular spectrum, in: Non-Commutative Harmonic Analysis, Lecture Notes in Mathematics No. 728, Springer-Verlag, Berlin-Heidelberg-New York, 1979. | MR 548330 | Zbl 0411.22015
and :[27] Shintani lifting and generalized Gelfand-Graev representations, Proc. Symp. Pure Math. 47 (1987), 147-163. | MR 933357 | Zbl 0654.20046
:[28] The primitive ideals associated to Harish-Chandra modules and certain harmonic polynomials, Thesis, M.I.T., 1979.
:[29] The character polynomial of the annihilator of an irreducible Harish-Chandra module, Amer. J. Math. 103 (1981), 1195-1240. | MR 636959 | Zbl 0486.17003
:[30] Commutativity of intertwining operators for semisimple groups, Compo. Math. 46 (1982), 33-84. | Numdam | MR 660154 | Zbl 0488.22027
:[31] Representation Theory of Semisimple Groups, An Overview Based on Examples, Princeton Mathematical series 36, Princeton University Press, Lawrenceville, New Jersey, 1986. | MR 855239 | Zbl 0604.22001
:[32] Classification theorems for representations of semisimple groups, in: Non-Commutative Harmonic Analysis, Lecture Notes in Mathematics, Vol. 587 (1977), 138-159. | MR 476923 | Zbl 0353.22011
and :[33] Classification of irreducible tempered representations of semisimple groups, Ann. of Math. 116 (1982), 389-501. | MR 672840 | Zbl 0516.22011
and :[34] The principal three dimensional subgroup and the Betti numbers of a complex simple Lie group, Amer. J. of Math. 81 (1959), 973-1032. | MR 114875 | Zbl 0099.25603
:[35] Lie group representations on polynomial rings, Amer. J. of Math. 86 (1963), 327-402. | MR 158024 | Zbl 0124.26802
:[36] On Whittaker vectors and representation theory, Invent. Math. 48 (1978), 101-184. | MR 507800 | Zbl 0405.22013
:[37] Orbits and representations associated with symmetric spaces, Amer. J. of Math. 93 (1971), 753-809. | MR 311837 | Zbl 0224.22013
and :[38] Finite- and infinite-dimensional representations of linear semisimple groups, Trans. Amer. Math. Soc. 184 (1973), 223-246. | MR 327978 | Zbl 0279.17001
and :[39] Induced unipotent classes, J. London Math. Soc. 19 (1979), 41-52. | MR 527733 | Zbl 0407.20035
and :[40] Generalized Whittaker vectors and representation theory, Thesis, M.I.T., 1979.
:[41] Some irreducible representations of Weyl groups, Bull. London Math. Soc. 4 (1972), 148-150. | MR 320171 | Zbl 0251.20043
:[42] Quelques remarques sur les groupes de Lie algébriques réels, J. Math. Soc. Japan 16 (1964), 419-446. | MR 183816 | Zbl 0133.28706
:[43] Boundary value problems for Whittaker functions on real split semisimple Lie groups, Duke Math. J. 53 (1986), 635-676. | MR 860664 | Zbl 0621.22011
:[44] Whittaker vectors and associated varieties, Invent. Math. 89 (1987), 219-224. | MR 892192 | Zbl 0633.17006
:[45] Cohomological Hardy space for SU(2, 2): Adv. Stud. in Pure Math. Vol. 14, Kinokuniya Book Store and North-Holland, 1986. | Zbl 0725.22006
:[46] Whittaker vectors and the Goodman-Wallach operators: Acta Math. 161 (1988), 183-241. | MR 971796 | Zbl 0723.22019
:[47] Whittaker modules associated with highest weight modules, Duke Math. J. 60 (1989), 59-113. Erratum, ibid. 61 (1990), 973. | MR 1047117 | Zbl 0716.17007
:[48] C-∞-Whittaker vectors for complex semisimple Lie groups, wave front sets, and Goldie rank polynomial representations, Ann. Scient. Ec. Norm. Sup. 23 (1990), 311-367. Erratum, ibid. 23 (1990), 668. | Numdam | Zbl 0760.22018
:[49] Modèles de Whittaker dénérés pour des groupes p-adiques, Math. Z. 196 (1987), 427-452. | Zbl 0612.22008
and :[50] Virtual character modules of semisimple Lie groups and representations of Weyl groups, J. Math. Soc. Japan 37, 719-740. | MR 806310 | Zbl 0589.22012
:[51] Orbital integrals in reductive Lie groups, Ann. of Math. 96 (1972), 505-510. | MR 320232 | Zbl 0302.43002
:[52] Modèle de Whittaker et caractères de representations, in: Non-Commutative Harmonic Analysis, Lecture Notes in Pure Mathematics No. 466, pp. 151-171, Springer-Verlag, Berlin-Heidelberg-New York, 1981. | MR 393355 | Zbl 0339.22014
:[53] Limit orbits in reductive Lie algebras, Duke Math. J. 49 (1982), 215-229. | MR 650378 | Zbl 0489.22019
:[54] Tempered representations and orbits, Duke Math. J. 49 (1982), 231-247. | MR 650379 | Zbl 0488.22019
:[55] Orbits in a real reductive Lie algebra, Trans. Amer. Math. Soc. 168 (1972), 403-421. | MR 349778 | Zbl 0222.17009
:[56] Microfunctions and pseudo-differential equations, in: Hyperfunctions and Pseudo-Differential Equations, Lecture Notes in Mathematics No. 287, pp. 264-529, Springer-Verlag, Berlin-Heidelberg-New York, 1971. | MR 420735 | Zbl 0277.46039
, , and :[57] Intégrales d'entrelacement et fonctions de Whittaker, Bull. Soc. Math. France 99 (1971), 3-72. | Numdam | MR 311838 | Zbl 0223.22017
:[58] On the characters of the discrete series (the Hermitian symmetric case), Invent. Math. 30 (1975), 47-144. | MR 396854 | Zbl 0324.22007
:[59] Two character identities for semisimple Lie groups, in: Non-Commutative Harmonic Analysis, Springer Lecture Notes in Math. Vol. 587, 1977, pp. 196-225. | MR 507247 | Zbl 0362.22015
:[60] Boundary value problems for group invariant differential equations, in: Proceedings of the Cartan Symposium, Lyon, 1984, Asterisque. | MR 837206 | Zbl 0621.22014
:[61] The nilpotent subvariety of the vector space associated to a symmetric pair, Publ. RIMS. Kyoto Univ. 20 (1984), 155-212. | MR 736100 | Zbl 0556.14022
:[62] Whittaker models for real groups, Duke Math. J. 47 (1980), 99-125. | MR 563369 | Zbl 0433.22007
:[63] The multiplicity one theorem for GL(n), Ann. of Math. 100 (1974), 171-193. | MR 348047 | Zbl 0316.12010
:[64] Reducibility of generalized principal series representations, Acta. Math. 145 (1980), 227-299. | MR 590291 | Zbl 0457.22011
and :[65] Introduction to Pseudodifferential and Fourier Integral Operators, Volume 1, Pseudodifferential Operators, Plenum Press, New York and London, 1980. | MR 597144 | Zbl 0453.47027
:[66] Gelfand-Kirillov dimensions for Harish-Chandra modules, Invent. Math. 48 (1978), 75-98. | MR 506503 | Zbl 0389.17002
:[67] Representations of Real Reductive Lie Groups, Progress in Mathematics, Birkhäuser, 1982. | Zbl 0469.22012
:[68] The orbit method and primitive ideals for semisimple Lie algebras, Canadian Mathematical Society Conference Proceedings Vol. 5 Lie Algebras and Related Topics (1986), 281-316. | MR 832204 | Zbl 0585.17008
:[69] Irreducible characters of semisimple Lie groups IV, character-multiplicity duality, Duke Math. J. 49 (1982), 943-1073. | MR 683010 | Zbl 0536.22022
:[70] Unitarizability of certain series of representations, Ann. of Math. 120 (1984), 141-187. | MR 750719 | Zbl 0561.22010
:[71] Representations of reductive Lie groups, in: Proceedings of the International Congress of Mathematics, Berkeley, California, USA, 1986. | Zbl 0681.22013
:[72] Asymptotic expansions of generalized matrix entries of representations of real reductive groups, in: Lie group representations I, Lecture Notes in Pure Mathematics No. 1024, pp. 287-369, Springer-Verlag, Berlin-Heidelberg-New York, 1983. | MR 727854 | Zbl 0553.22005
:[73] Real Reductive Groups I, Academic Press, 1987. | MR 929683 | Zbl 0666.22002
:[74] Lie algebra cohomology and holomorphic continuation of generalized Jacquet integrals, Adv. Stud. in Pure Math. Vol. 14, pp. 123-151, Kinokuniya Book Store, 1986. | MR 1039836 | Zbl 0714.17016
:[75] Harmonic Analysis on Semi-Simple Lie Groups I, Die Drundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Band 188, Springer-Verlag, Berlin-Heidelberg -New York, 1972. | MR 498999 | Zbl 0265.22020
:[76] Multiplicity one theorems for generalized Gelfand-Graev representations of semisimple Lie groups and Whittaker models for the discrete series, Adv. Stud. in Pure Math. Vol. 14, pp. 31-121, Kinokuniya Book Store, 1986. | MR 1039835 | Zbl 0759.22018
:[77] Tensor products of finite and infinite dimensional representations of semisimple Lie groups, Ann. of Math. 106 (1977), 295-308. | MR 457636 | Zbl 0384.22004
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