Whittaker models, nilpotent orbits and the asymptotics of Harish-Chandra modules
Compositio Mathematica, Volume 96 (1995) no. 1, pp. 1-62.
@article{CM_1995__96_1_1_0,
author = {Collingwood, David H.},
title = {Whittaker models, nilpotent orbits and the asymptotics of {Harish-Chandra} modules},
journal = {Compositio Mathematica},
pages = {1--62},
volume = {96},
number = {1},
year = {1995},
zbl = {0834.22016},
mrnumber = {1323724},
language = {en},
url = {http://archive.numdam.org/item/CM_1995__96_1_1_0/}
}
TY  - JOUR
AU  - Collingwood, David H.
TI  - Whittaker models, nilpotent orbits and the asymptotics of Harish-Chandra modules
JO  - Compositio Mathematica
PY  - 1995
DA  - 1995///
SP  - 1
EP  - 62
VL  - 96
IS  - 1
UR  - http://archive.numdam.org/item/CM_1995__96_1_1_0/
UR  - https://zbmath.org/?q=an%3A0834.22016
UR  - https://www.ams.org/mathscinet-getitem?mr=1323724
LA  - en
ID  - CM_1995__96_1_1_0
ER  - 
%0 Journal Article
%A Collingwood, David H.
%T Whittaker models, nilpotent orbits and the asymptotics of Harish-Chandra modules
%J Compositio Mathematica
%D 1995
%P 1-62
%V 96
%N 1
%G en
%F CM_1995__96_1_1_0
Collingwood, David H. Whittaker models, nilpotent orbits and the asymptotics of Harish-Chandra modules. Compositio Mathematica, Volume 96 (1995) no. 1, pp. 1-62. http://archive.numdam.org/item/CM_1995__96_1_1_0/

[1] D. Barbasch and D. Vogan: Primitive ideals and orbital integrals in complex exceptional groups, J. Algebra 80 (1983) 350-382. | MR | Zbl

[2] B. Boe and D. Collingwood: A multiplicity one theorem for holomorphically induced representations, Math. Z. 192 (1986) 265-282. | MR | Zbl

[3] B. Boe and D. Collingwood: Multiplicity free categories of highest weight representations I, Comm. Alg. 18 (1990) 947-1032. | MR | Zbl

[4] B. Boe and D. Collingwood: Multiplicity free categories of highest weight representations II, Comm. Alg. 18 (1990) 1033-1070. | MR | Zbl

[5] B. Boe and D. Collingwood: Enright-Shelton theory and Vogan's problem for generalized principal series, Mem. Amer. Math. Soc. 486 (1993). | MR | Zbl

[6] W. Borho: Lie Algebras and Related Topics. Canadian Math. Soc. Conf. Proc. 5, Providence, 1986. | MR

[7] L. Casian and D. Collingwood: The Kazhdan-Lusztig conjecture for generalized Verma modules, Math. Z. 195 (1987) 581-600. | MR | Zbl

[8] L. Casian and D. Collingwood: Complex geometry and asymptotics for Harish-Chandra modules of real reductive Lie groups I, Trans. Amer. Math. Soc. 300 (1987) 73-107. | MR | Zbl

[9] L. Casian and D. Collingwood: Complex geometry and asymptotics for Harish-Chandra modules of real reductive Lie groups II, Invent. Math. 86 (1986) 255-286. | MR | Zbl

[10] L. Casian and D. Collingwood: Complex geometry and asymptotics for Harish-Chandra modules of real reductive Lie groups III: Estimates on n-homology, J. Algebra 116 (1988) 415-456. | MR | Zbl

[11] L. Casian and D. Collingwood: Weight filtrations for induced representations of real reductive Lie groups, Adv. Math. 73 (1989) 79-146. | MR | Zbl

[12] D. Collingwood: Harish-Chandra modules with the unique embedding property, Trans. Amer. Math. Soc. 281 (1984) 1-48. | MR | Zbl

[13] D. Collingwood: Representations of rank one Lie groups, Pitman, Boston, 1985. | MR | Zbl

[14] D. Collingwood: Representations of rank one Lie groups II, Mem. Amer. Math. Soc. 387 (1988). | MR | Zbl

[15] D. Collingwood: Jacquet modules for semisimple Lie groups having Verma module filtrations, J. Algebra 136 (1991) 353-375. | MR | Zbl

[16] D. Collingwood, R. Irving and B. Shelton: Filtrations on generalized Verma modules for Hermitian symmetric pairs, J. reine angew. Math. 383 (1988) 54-86. | MR | Zbl

[17] D. Collingwood and W. Mcgovern: Nilpotent Orbits in Semisimple Lie Algebras, Van Nostrand Reinhold, New York, 1993. | MR | Zbl

[18] D. Garfinkle: The annihilators of irreducible Harish-Chandra modules for SU(p, q) and other type An-1 groups, Amer. J. Math. 115 (1993) 305-369. | MR | Zbl

[19] R. Goodman and N. Wallach: Whittaker vectors and conical vectors, J. Funct. Anal. 39 (1980) 199-279. | MR | Zbl

[20] H. Hecht and W. Schmid: Characters, asymptotics and n-homology of Harish-Chandra modules, Acta Math. 151 (1983) 49-151. | MR | Zbl

[21] R. Irving: Projective modules in the category Os: Self-duality, Trans. Amer. Math. Soc. 291 (1985) 701-732. | Zbl

[22] B. Kostant: On Whittaker vectors and representation theory, Invent. Math. 48 (1978) 101-184. | MR | Zbl

[23] G. Lusztig: A class of irreducible representations of a Weyl group II, Indag. Math. 44 (1982) 219-226. | MR | Zbl

[24] G. Lusztig and D. Vogan: Singularities of closures of K-orbits on flag manifolds, Inv. Math. 71 (1983) 365-379. | MR | Zbl

[25] H. Matumoto: Whittaker vectors and associated varieties, Invent. Math. 89 (1987) 219-224. | MR | Zbl

[26] H. Matumoto: Whittaker vectors and the Goodman-Wallach operators, Acta Math. 161 (1988) 183-241. | Zbl

[27] H. Matumoto: 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. | Numdam | Zbl

[28] H. Matumoto: C-∞-Whittaker vectors corresponding to a principal nilpotent orbit of a real reductive linear Lie group, and wave front sets, Comp. Math. 82 (1992) 189-244. | Numdam | Zbl

[29] R. Proctor: Classical Bruhat orders and lexicographic shellability, J. Algebra 77 (1982) 104-126. | MR | Zbl

[30] W. Soergel: Equivalences de certaines de g-modules, C.R. Acad. Sci. Paris 303 (1986). | MR | Zbl

[31] D. Vogan: Gelfand-Kirillov dimensions for Harish-Chandra modules, Invent. Math. 48 (1978) 75-98. | MR | Zbl

[32] D. Vogan: Representations of real reductive Lie groups, Birkhäuser, Boston, 1981. | MR | Zbl

[33] D. Vogan: Irreducible characters of semisimple Lie groups III: proof of the Kazhdan-Lustig conjectures in the integral case, Inv. Math. 71 (1983) 381-417. | MR | Zbl

[34] D. Vogan: Irreducible characters of semisimple Lie groups IV: character multiplicity duality, Duke Math. J. 49 (1982) 943-1073. | MR | Zbl