C - -Whittaker vectors for complex semisimple Lie groups, wave front sets, and Goldie rank polynomial representations
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 23 (1990) no. 2, p. 311-367
@article{ASENS_1990_4_23_2_311_0,
     author = {Matumoto, Hisayosi},
     title = {$C^{-\infty }$-Whittaker vectors for complex semisimple Lie groups, wave front sets, and Goldie rank polynomial representations},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Elsevier},
     volume = {Ser. 4, 23},
     number = {2},
     year = {1990},
     pages = {311-367},
     doi = {10.24033/asens.1605},
     zbl = {0760.22017},
     mrnumber = {91i:22020},
     language = {en},
     url = {http://www.numdam.org/item/ASENS_1990_4_23_2_311_0}
}
Matumoto, Hisayosi. $C^{-\infty }$-Whittaker vectors for complex semisimple Lie groups, wave front sets, and Goldie rank polynomial representations. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 23 (1990) no. 2, pp. 311-367. doi : 10.24033/asens.1605. http://www.numdam.org/item/ASENS_1990_4_23_2_311_0/

[BV1] D. Barbasch and D. A. Vogan Jr., The Local Structure of Characters (J. Funct. Anal., vol. 37, 1980, pp. 27-55). | MR 82e:22024 | Zbl 0436.22011

[BV2] D. Barbasch and D. A. Vogan Jr., Primitive Ideals and Orbital Integrals in Complex Classical Groups (Math. Ann. Vol. 259, 1982, pp. 153-199). | MR 83m:22026 | Zbl 0489.22010

[BV3] D. Barbasch and D. A. Vogan Jr., Primitive Ideals and Orbital Integrals in Complex exceptional Groups (J. Algebra, Vol. 80, 1983, pp. 350-382). | MR 84h:22038 | Zbl 0513.22009

[BV4] D. Barbasch and D. A. Vogan Jr., Unipotent Representations of Complex Semisimple Lie Groups (Ann, of Math., Vol. 121, 1985, pp. 41-110). | Zbl 0582.22007

[BV5] D. Barbasch and D. A. Vogan Jr., Weyl Group Representations and nilpotent Orbits, in : P. C. TROMBI, editor, "Representation Theory of Reductive Groups" (Progress in Mathematics, Vol. 40, pp. 21-33, Birkhäuser, Boston-Basel-Stuttgart, 1983). | MR 85g:22025 | Zbl 0537.22013

[BeG] J. Bernstein and S. I. Gelfand, Tensor Product of Finite and Infinite Dimensional Representations of Semisimple Lie Algebras (Compos. Math., 41, 1980, pp. 245-285). | Numdam | MR 82c:17003 | Zbl 0445.17006

[BeyL] W. M. Beynon and G. Lusztig, Some Numerical Results on the Characters of Exceptional Weyl Groups (Math. Soc. Camb. Phil. Soc., Vol. 84, 1978, pp. 417-426). | MR 80a:20017 | Zbl 0416.20033

[BW] A. Borel and N. R. Wallach, "Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups." (Annals of Mathematics Studies, Princeton University Press, Princeton, NJ, 1980). | MR 83c:22018 | Zbl 0443.22010

[BoBr] W. Borho and J.-L. Brylinski, Differential Operators on Homogeneous Spaces III (Invent. Math., Vol. 80, 1985, pp. 1-68). | MR 87i:22045 | Zbl 0577.22014

[BoBrM] W. Borho, J.-L. Brylinski and R. D. Macpherson, Nilpotent Orbits, Primitive Ideals, and Characteristic Classes, preprint, Max-Planck-Institut für Mathematik, Bonn, January, 1988. | Zbl 0697.17006

[BoKr] W. Borho and H. Kraft, Uber primitive ideale in der Einhüllenden einer halbeinfachen Lie-Algebra (Invent. Math., Vol. 39, 1977, pp. 1-53). | Zbl 0327.17002

[BoM1] W. Borho and R. D. Macpherson, Représentations des groupes de Weyl et homologie d'intersection pour les variétés nilpotentes (C.R. Acad. Sci. Paris, T. 292, 1981, pp. 707-710). | MR 82f:14002 | Zbl 0467.20036

[BoM2] W. Borho and R. D. Macpherson, Partial Resolutions of Nilpotent Varieties (Astérisque, Vol. 101-102, 1983, pp. 23-74). | MR 85j:14087 | Zbl 0576.14046

[Ca1] W. Casselman, A letter to Harish-Chandra, November 30, 1982.

[Ca2] W. Casselman, Jacquet Modules for Real Reductive groups, in : Proceedings of the International Congress of Mathematics, Helsinki, 1978, pp. 557-563. | MR 83h:22025 | Zbl 0425.22019

[Ca3] W. Casselman, Canonical Extensions of Harish-Chandra Modules to Representations of G, preprint. | Zbl 0702.22016

[CD] N. Conze-Berline and M. Duflo, Sur les représentations induites des groupes semi-simples complexes (Compos. Math., Vol. 34, 1977, pp. 307-336). | Numdam | MR 55 #12872 | Zbl 0389.22016

[D1] M. Duflo, Représentations irréductibles des groupes semi-simples complexes, pp. 26-88 in : Analyse Harmonique sur les Groupes de Lie (Lect. Notes Math., No. 497, Springer-Verlag, Berlin-Heidelberg-New York, 1975). | MR 53 #3198 | Zbl 0315.22008

[D2] M. Duflo, Sur la classifications des idéaux primitifs dans l'algèbre de Lie semi-simple (Ann. Math., Vol. 1977, pp. 107-120). | MR 55 #3013 | Zbl 0346.17011

[D3] M. Duflo, Polynômes de Vogan pour SL(n, C), pp. 64-76 in : Non-Commutative Harmonic Analysis (Lecture Notes in Mathematics, No. 728, Springer-Verlag, Berlin-Heidelberg-New York, 1979). | MR 81b:22015 | Zbl 0414.22018

[GJ] O. Gabber and A. Joseph, Oh the Bernstein-Gelfand-Gelfand Resolution and the Duflo sum Formula (Compos. Math., Vol. 43, 1981, pp. 107-131). | Numdam | MR 82k:17009 | Zbl 0461.17004

[GG1] I. M. Gelfand and M. I. Graev, Categories of Group Representations and the Problem of Classifying Irreducible Representations (Soviet Math. Dokl., Vol. 3, 1962, pp. 1382-1385).

[GG2] I. M. Gelfand and M. I. Graev, Construction of Irreducible Representations of Simple Algebraic Groups Over a Finite field (Soviet Math. Dokl., Vol. 3, 1962, pp. 1646-1649). | MR 26 #6271 | Zbl 0119.26901 | Zbl 0119.26902

[Gi] V. Ginsburg, G-modules, Springer's Representations and bivariant Chern Classes (Adv. Math., Vol. 61, 1986, pp. 1-48). | MR 87k:17014 | Zbl 0601.22008

[Go] R. Goodman, Horospherical Functions on Symmetric Spaces (Canadian Matehatical Society Conference Proceedings Vol. 1, 1981, pp. 125-133). | Zbl 0545.43008

[GW] R. Goodman and N. R. Wallach, Whittaker Vectors and Conical Vectors (J. Funct. Anal., Vol. 39, 1980, pp. 199-279). | MR 82i:22018 | Zbl 0475.22010

[GorM] M. Goresky and R. Macpherson, "Stratified Morse Theory", Springer-Verlag, Berlin-Heidelberg-New York-London-Paris-Tokyo, 1980.

[Ha1] M. Hashizume, Whittaker models for semisimple Lie groups (Jpn J. Math., Vol. 5, 1979, pp. 349-401). | MR 82g:10048 | Zbl 0506.22016

[Ha2] M. Hashizume, Whittaker Models for Representations with Highest Weights, in : Lectures on Harmonic analysis on Lie Groups and Related Topics (Strasbourg, 1979, pp. 45-50, Lect. Math., Vol. 14, Kinokuniya Book Store, Tokyo, 1982). | Zbl 0596.22005

[Ha3] M. Hashizume, Whittaker Functions on Semisimple Lie Groups (Hiroshima Math. J., Vol. 13, 1982, pp. 259-293). | MR 84d:22018 | Zbl 0524.43005

[He] S. Helgason, A Duality for Symmetric Spaces with Applications to Group Representations (Adv. Math., Vol. 5, 1970, pp. 1-154). | MR 41 #8587 | Zbl 0209.25403

[HS] P. J. Hilton and U. Stammbach, "A Course in Homological Algebra", GTM No. 4, Springer-Verlag, Berlin-Heidelberg-New York, 1970. | Zbl 0238.18006

[Hi1] H. Hironaka, Resolution of Singularities of an algebraic geometry over a field of Characteristic 0 (Ann. Math., Vol. 79, 1964, pp. 109-326). | MR 33 #7333 | Zbl 0122.38603

[Hi2] H. Hironaka, Subanalytic sets, in : "Number Theory, Algebraic Geometry and Commutative Algebra, in honor of Y. AKIZUKI", pp. 453-493, Kinokuniya Book Store, Tokyo, 1973. | MR 51 #13275 | Zbl 0297.32008

[Hör] L. Hörmander, Fourier Integral Operators I (Acta Math., Vol. 127, 1971, pp. 79-183). | MR 52 #9299 | Zbl 0212.46601

[Hot1] R. Hotta, On Springer's Representations (J. Fac. Sci. Univ. Tokyo, IA Vol. 28, 1982, pp. 863-876). | MR 83h:20038 | Zbl 0584.20033

[Hot2] R. Hotta, On Joseph's Construction of Weyl Group Representations (Tohoky Math. J., Vol. 36, 1984, pp. 49-74). | MR 86h:20061 | Zbl 0545.20029

[Hot3] R. Hotta, A local formula for Springer's Representation (Adv. Stud. Pure Math., Vol. 6, 1985, pp. 127-138). | MR 87b:20059 | Zbl 0571.20033

[HotK] R. Hotta and Masaki Kashiwara, The Invariant Holonomic System on a Semisimple Lie algebra (Invent. Math., Vol. 75, 1984, pp. 327-358). | MR 87i:22041 | Zbl 0538.22013

[How] R. Howe, Wave Front Sets of Representations of Lie Groups, in "Automorphic Forms, Representation Theory, and Arithmetic", Bombay, 1981. | MR 83c:22014 | Zbl 0494.22010

[Ja] H. Jacquet, Fonction de Whittaker associées aux groupes de Chevalley (Bull. Soc. Math. France, Vol. 95, 1967, pp. 243-309). | Numdam | MR 42 #6158 | Zbl 0155.05901

[JL] H. Jacquet and R. P. Langlands, "Automorphic Form on GL (2)" (Lect. Notes Math., No. 114, Springer-Verlag, Berlin-Heidelberg-New York). | MR 53 #5481 | Zbl 0236.12010

[Jo1] A. Joseph, On the Annihilators of the Simple Subquotients of the Principal series (Ann. Scient. Éc. Norm. Sup. (4), Vol. 10, 1977, pp. 419-440). | Numdam | MR 58 #809 | Zbl 0386.17004

[Jo2] A. Joseph, Dixmier's problem for Verma and Principal Series Submodules (J. London Math. Soc., (2), Vol. 20, 1979, pp. 193-204). | MR 81c:17016 | Zbl 0421.17005

[Jo3] A. Joseph, W-module Structures in the Primitive Spectrum of the Enveloping Algebra of a Semisimple Lie Algebra, pp. 116-135 in : Non-Commutative Harmonic Analysis (Lect. Notes Math., No. 728, Springer-Verlag, Berlin-Heidelberg-New York, 1979). | MR 80k:17007 | Zbl 0422.17004

[Jo4] A. Joseph, Towards the Jantzen conjecture I (Compos. Math., Vol. 40, 1980, pp. 35-67). | Numdam | MR 81m:17013a | Zbl 0424.17004

[Jo5] A. Joseph, Towards the Jantzen conjecture II (Compos. Math., Vol. 40, 1980, pp. 69-78). | Numdam | MR 81m:17013a | Zbl 0424.17005

[Jo6] A. Joseph, Kostant's Problem, Goldie rank and Gelfand-Kirillov Conjecture (Invent. Math., Vol. 56, 1980, pp. 191-213). | MR 82f:17008 | Zbl 0446.17006

[Jo7] A. Joseph, Goldie Rank in the Enveloping Algebra of a Semisimple Lie Algebra I (J. Algebra, Vol. 65, 1980, pp. 269-283). | MR 82f:17009 | Zbl 0441.17004

[Jo8] A. Joseph, Goldie Rank in the Enveloping Algebra of a Semisimple Lei Algebra II (J. Algebra, Vol. 65, 1980, pp. 284-306). | MR 82f:17009 | Zbl 0441.17004

[Jo9] A. Joseph, Goldie rank in the enveloping algebra of a semisimple Lie algebra III (J. Algebra, Vol. 73, 1981, pp. 295-326). | MR 83k:17010 | Zbl 0482.17002

[Jo10] A. Joseph, Towards the Jantzen conjecture III (Compos. Math., Vol. 41, 1981, pp. 23-30). | Numdam | MR 81m:17013b | Zbl 0446.17005

[Jo11] A. Joseph, On the Classification of Primitive Ideals in the enveloping Algebra of a samisimple Lie Algebra, pp. 30-76 in : Lect. Notes Math., No. 1024, Springer-Verlag, Berlin-Heidelberg-New York, 1983. | MR 85b:17008 | Zbl 0518.17003

[Jo12] A. Joseph, On the Cyclicity of vectors Associated with Duflo Involutions, pp. 145-188 in : Non-Commutative Harmonic Analysis (Lect. Notes Math., No. 1243, Springer-Verlag, Berlin-Heidelberg-New York, 1986). | Zbl 0621.17006

[Kas] M. Kashiwara, The Riemann-Hilbert Problem for Holonomic Systems, Publ. R.I.M.S., Kyoto Univ., Vol. 20, 1984, pp. 319-365. | MR 86j:58142 | Zbl 0566.32023

[KV1] M. Kashiwara and M. Vergne, 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 81e:22022 | Zbl 0416.22006

[KV2] M. Kashiwara and M. Vergne, K-types and the Singular Spectrum, in : Non-Commutative Harmonic Analysis (Lect. Notes Math., No. 728, Springer-Verlag, Berlin-Heidelberg-New York, 1979). | MR 81m:22022 | Zbl 0411.22015

[KT] M. Kashiwara and T. Tanisaki, The Characteristic cycles of Holomomic Systems on a Flag Manifold-related to the Weyl Group Algebra (Invent. Math., Vol. 77, 1984, pp. 185-198). | MR 86m:17015 | Zbl 0611.22008

[Kaw1] N. Kawanaka, Generalized Gelfand-Graev Representations and Ennola Duality, in “Algebraic Groups and Related Topics” (Adv. Stud. Pure Math., Vol. 6, Kinokuniya Book Store and North-Holland, 1985, pp. 175-206). | MR 87e:20075 | Zbl 0573.20038

[Kaw2] N. Kawanaka, Generalized Gelfand-Graev Representations of Exceptional Simple Algebraic Groups over a Finite field I (Invent. Math., Vol. 84, 1986, pp. 575-616). | MR 88a:20058 | Zbl 0596.20028

[Kaw3] N. Kawanaka, Shintani lifting and Generalized Gelfand-Graev Representations (Proc. Symp. Pure Math., Vol. 47, 1987, pp. 147-163). | MR 89h:22037 | Zbl 0654.20046

[KL1] D. A. Kazhdan and G. Lusztig, Representations of Coxeter Groups and Hecke Algebras (Invent. Math. Vol. 53, 1979, pp. 165-184). | MR 81j:20066 | Zbl 0499.20035

[KL2] D. A. Kazhdan and G. Lusztig, A topological Approach to Springer's Representations (Adv. Math., Vol. 38, 1980, pp. 222-228). | MR 82f:20076 | Zbl 0458.20035

[Ki1] D. R. King, The Primitive Ideals assoated to Harish-Chandra Modules and Certain harmonic Polynomials. (Thesis, M.I.T., 1979).

[Ki2] D. R. King, The Character Polynomial of the Annihilator of an Irreducible Harish-Chandra Module (Am. J. Math., Vol. 103, 1981, pp. 1195-1240). | MR 83d:22010a | Zbl 0486.17003

[Kn] A. W. Knapp, “Representation Theory of Semisimple Groups, An Overview Based on Examples”, Princeton Mathematical series 36, Princeton University Press, Lawrenceville, New Jersey, 1986. | MR 87j:22022 | Zbl 0604.22001

[Ko1] B. Kostant, Lie algebra Cohomology and the Generalized Borel-Weil Theorem (Ann. Math., Vol. 48, 1978, pp. 101-184). | MR 80b:22020

[Ko2] B. Kostant, On Whittaker Vectors and Representation Theory (Invent. Math., Vol. 48, 1978, pp. 101-184). | MR 80b:22020 | Zbl 0405.22013

[Le] J. Lepowski, Generalized Verma Modules, the Cartan-Helgason Theorem, and the Harish-Chandra Homomorphism (J. Algebra, Vol. 49, 1977, pp. 470-495). | MR 57 #3312 | Zbl 0381.17005

[LeW] J. Lepowski and N. R. Wallach, Finite- and Infinite-dimensional Representations of Linear Semisimple Groups (Trans. Am. Math. Soc., Vol. 184, 1973, pp. 223-246). | MR 48 #6320 | Zbl 0279.17001

[Lo] S. Lojasiewicz, Sur le problème de la division (Studia Math.), 8, 1959, pp. 87-136). | MR 21 #5893 | Zbl 0115.10203

[Lu1] G. Lusztig, On a Theorem of Benson and Curtis (J. Algebra Vol. 71, 1981, pp. 490-498). | MR 83a:20053 | Zbl 0465.20042

[Lu2] G. Lusztig, A Class of Irreducible Representations of a Weyl Group (Proc. Kon. Nederl. Akad., series A, Vol. 82, 1979, pp. 323-335). | MR 81a:20052 | Zbl 0435.20021

[Lu3] G. Lusztig, A class of Irreducible Representations of a Weyl Group II (Proc. Kon. Nederl. Akad., series A, Vol. 85, 1982, pp. 219-226). | MR 83h:20018 | Zbl 0511.20034

[Lu4] G. Lusztig, “Characters of Reductive Groups over a Finite field” (Annals of Mathematics Studies, No. 107, Princeton University Press, Princeton, New Jersey, 1984). | MR 86j:20038 | Zbl 0556.20033

[Lu5] G. Lusztig, Cells in Affine Weyl Groups, in : Advanced Studies in Pure Math., Vol. 6, Kinokuniya Book Store and North-Holland, 1985. | MR 87h:20074 | Zbl 0569.20032

[Lu6] G. Lusztig, Cells in Affine Weyl Groups II (J. Algebra, Vol. 109, 1987, pp. 536-548). | MR 88m:20103a | Zbl 0625.20032

[Lu7] G. Lusztig, Leading Coefficients of Character Values of Hecke Algebras (Proc. Symp. Pure Math., Vol. 47, 1987, pp. 235-262). | MR 89b:20087 | Zbl 0657.20037

[LuN] G. Lusztig and Xi Nanhua, Canonical Left Cells in Affine Weyl groups (Adv. Math., Vol. 72, 1988, pp. 284-288). | MR 89m:17027 | Zbl 0664.20028

[Ly] T. E. Lynch, Generalized Whittaker Vectors and Representation Theory (Thesis, M.I.T., 1979).

[Mac] I. G. Macdonald, Some Irreducible Representations of Weyl Groups (Bull. London Math. Soc., Vol. 4, 1972, pp. 148-150). | MR 47 #8710 | Zbl 0251.20043

[Mar] A. Martineau, Distributions et valeurs au bord des fonctions holomorphes, œuvre de André Martineau, Paris, C.N.R.S., 1977, pp. 439-582.

[Mat1] H. Matumoto, Boundary Value Problems for Whittaker Functions on Real Split Semisimple Lie Groups (Duke Math. J., Vol. 53, 1986, pp. 635-676). | MR 88b:22010 | Zbl 0621.22011

[Mat2] H. Matumoto, Whittaker Vectors and Associated Varieties (Invent. Math., Vol. 89, 1987, pp. 219-224). | MR 88k:17022 | Zbl 0633.17006

[Mat3] H. Matumoto, Cohomological Hardy Space for SU (2,2),, to appear in : Adv. Stud. Pure Math., Vol. 14, Kinokuniya Book Store and North-Holland. | MR 91c:22032 | Zbl 0725.22006

[Mat4] H. Matumoto, Whittaker Vectors and the Goofman-Wallach Operators, to appear in Acta Math. | Zbl 0723.22019

[Mat5] H. Matumoto, Whittaker Vectors and Whittaker Functions for real Semisimple Lie Groups (Theisis, M.I.T., 1988).

[Mœ1] C. Mœglin, Modèles de Whittaker et idéaux primitifs complètement premiers dans les algèbres enveloppantes (C. R. Acad. Sci. Paris, Vol. 303, 1986, pp. 845-848). | MR 87m:17020 | Zbl 0628.17007

[Mœ2] C. Mœglin, Modèles de Whittaker et idéaux primitifs complètement premiers dans les algèbres enveloppantes I, preprint, 1986. | Zbl 0628.17007

[Mœ3] C. Mœglin, Modèles de Whittaker et idéaux primitifs complètement premiers dans les algèbres enveloppantes des algèbres de Lie semisimple complexes II, preprint 1986. | Zbl 0714.17012

[MW] C. Mœglin and J. L. Waldspurger, Modèles de Whittaker dégénérés pour des groupes p-adiques (Math. Z., Vol. 196, 1987, pp. 427-452). | MR 89f:22024 | Zbl 0612.22008

[OW] H. Ozeki and M. Wakimoto, On Polarizations of Certain Homogeneous Spaces (Hiroshima Math., J., Vol. 2, 1972, pp. 445-482). | MR 49 #5236a | Zbl 0244.22013 | Zbl 0267.22011

[R] F. Rodier, 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 52 #14165 | Zbl 0339.22014

[Sc] G. Schiffmann, Intégrales d'entrelacement et fonctions de Whittaker (Bull. Soc. Math. France, Vol. 99, 1971, pp. 3-72). | Numdam | MR 47 #400 | Zbl 0223.22017

[Sch] L. Schwartz, “Théorie des distributions” Hermann, Paris, 1950. | Zbl 0037.07301

[Sh] G. Shalika, The Multiplicity one Theorem for GL(n) (Ann. Math., Vol. 100, 1974, pp. 171-193). | MR 50 #545 | Zbl 0316.12010

[Sp1] T. A. Springer, Trigonometric sums, Green Functions of finite Groups and Representations of Weyl Groups (Invent. Math., Vol. 36, 1976, pp. 173-207). | MR 56 #491 | Zbl 0374.20054

[Sp2] T. A. Springer, A construction of Representations of Weyl Groups (Invent. Math., Vol. 44, 1978, pp. 279-293). | MR 58 #11154 | Zbl 0376.17002

[T] F. Treves, “Introduction to Pseudodifferential and Fourier Integral Operators”, Vol. 1, Pseudodifferential Operators, Plenum Press, New York and London, 1980. | Zbl 0453.47027

[Vo1] D. A. Vogan Jr., Gelfand-Kirillov Dimension for Harish-Chandra Modules (Invent. Math., Vol. 48, 1978, pp. 75-98). | MR 58 #22205 | Zbl 0389.17002

[Vo2] D. A. Vogan Jr., Ordering of the Primitive Spectrum of a Semisimple Lie Algebra (Math. Ann., Vol. 248, pp. 195-203). | MR 81k:17006 | Zbl 0414.17006

[Vo3] D. A. Vogan Jr., “Representations of Real Reductive Lie Groups” (Progress in Mathematics, Birkhäuser, 1982). | Zbl 0469.22012

[Vo4] D. A. Vogan Jr., The Orbit Method and Primitive Ideals for Semisimple Lie Algebras (Canadian Mathematical Society Conference Proceedings, Vol. 5 “Lie Algebras and Related Topics”, 1986, pp. 381-316). | MR 87k:17015 | Zbl 0585.17008

[Vo5] D. A. Vogan Jr., Irreduicible Characters of Semisimple Lei Groups IV, Character-multiplicity duality (Duke Math. J., Vol. 49, 1982, pp. 943-1073). | Zbl 0536.22022

[W1] N. R. Wallach, Asymptotic Expansions of Generalized Matrix Entries of Representations of Real Reductive Groups, in : Lie group Representations I (Lecture Notes Pure Math., No. 1024, pp. 287-369, Springer-Verlag, Berlin-Heidelberg-New York, 1983). | MR 85g:22029 | Zbl 0553.22005

[W2] N. R. Wallach, “Real reductive Groups I”, Academic press, 1987. | Zbl 0666.22002

[W3] N. R. Wallach, Lie Algebra Cohomology and Holomorphic Continuation of Generalized Jacquet Integrals, to appear in : Adv. Stud. Pure Math., Vol. 14, Kinokuniya Book Store and North-Holland. | MR 91d:22014 | Zbl 0714.17016

[War] G. Warner, “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 58 #16979 | Zbl 0265.22020

[Y1] H. Yamashita, On Whittaker Vectors for Generalized Gelfand-Graev Representations of Semisimple Lie Groups (J. Math. Kyoto Univ., Vol. 26, 1986, pp. 263-298). | MR 88a:22028 | Zbl 0613.22002

[Y2] H. Yamashita, Multiplicity one Theorems for Generalized Gelfand-Graev Representations of Semi-simple Lie Groups and Whittaker Models for the Discrete Series, priprint, 1987.