Whittaker models, nilpotent orbits and the asymptotics of Harish-Chandra modules
Compositio Mathematica (1995)
- Volume: 96, Issue: 1, page 1-62
- ISSN: 0010-437X
Access Full Article
topHow to cite
topCollingwood, David H.. "Whittaker models, nilpotent orbits and the asymptotics of Harish-Chandra modules." Compositio Mathematica 96.1 (1995): 1-62. <http://eudml.org/doc/90355>.
@article{Collingwood1995,
author = {Collingwood, David H.},
journal = {Compositio Mathematica},
keywords = {subrepresentation theorem; Langlands classification; nonmaximal embeddings; irreducible admissible representation; semisimple Lie group; principal series representation; Whittaker models; Matumoto's conjecture; irreducible Harish-Chandra modules; matrix coefficient asymptotics; matrix groups; nilpotent orbit condition},
language = {eng},
number = {1},
pages = {1-62},
publisher = {Kluwer Academic Publishers},
title = {Whittaker models, nilpotent orbits and the asymptotics of Harish-Chandra modules},
url = {http://eudml.org/doc/90355},
volume = {96},
year = {1995},
}
TY - JOUR
AU - Collingwood, David H.
TI - Whittaker models, nilpotent orbits and the asymptotics of Harish-Chandra modules
JO - Compositio Mathematica
PY - 1995
PB - Kluwer Academic Publishers
VL - 96
IS - 1
SP - 1
EP - 62
LA - eng
KW - subrepresentation theorem; Langlands classification; nonmaximal embeddings; irreducible admissible representation; semisimple Lie group; principal series representation; Whittaker models; Matumoto's conjecture; irreducible Harish-Chandra modules; matrix coefficient asymptotics; matrix groups; nilpotent orbit condition
UR - http://eudml.org/doc/90355
ER -
References
top- [1] D. Barbasch and D. Vogan: Primitive ideals and orbital integrals in complex exceptional groups, J. Algebra80 (1983) 350-382. Zbl0513.22009MR691809
- [2] B. Boe and D. Collingwood: A multiplicity one theorem for holomorphically induced representations, Math. Z.192 (1986) 265-282. Zbl0598.22009MR840829
- [3] B. Boe and D. Collingwood: Multiplicity free categories of highest weight representations I, Comm. Alg.18 (1990) 947-1032. Zbl0757.17005MR1059940
- [4] B. Boe and D. Collingwood: Multiplicity free categories of highest weight representations II, Comm. Alg.18 (1990) 1033-1070. Zbl0757.17005MR1059940
- [5] B. Boe and D. Collingwood: Enright-Shelton theory and Vogan's problem for generalized principal series, Mem. Amer. Math. Soc.486 (1993). Zbl0794.22010MR1129375
- [6] W. Borho: Lie Algebras and Related Topics. Canadian Math. Soc. Conf. Proc.5, Providence, 1986. MR832193
- [7] L. Casian and D. Collingwood: The Kazhdan-Lusztig conjecture for generalized Verma modules, Math. Z.195 (1987) 581-600. Zbl0624.22010MR900346
- [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. Zbl0657.22016MR871666
- [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. Zbl0657.22017MR856846
- [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. Algebra116 (1988) 415-456. Zbl0723.22016MR953161
- [11] L. Casian and D. Collingwood: Weight filtrations for induced representations of real reductive Lie groups, Adv. Math.73 (1989) 79-146. Zbl0676.22011MR979588
- [12] D. Collingwood: Harish-Chandra modules with the unique embedding property, Trans. Amer. Math. Soc.281 (1984) 1-48. Zbl0536.22019MR719657
- [13] D. Collingwood: Representations of rank one Lie groups, Pitman, Boston, 1985. Zbl0647.22007MR853731
- [14] D. Collingwood: Representations of rank one Lie groups II, Mem. Amer. Math. Soc.387 (1988). Zbl0657.22015MR954949
- [15] D. Collingwood: Jacquet modules for semisimple Lie groups having Verma module filtrations, J. Algebra136 (1991) 353-375. Zbl0716.22005MR1089304
- [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. Zbl0631.22014MR921987
- [17] D. Collingwood and W. McGovern: Nilpotent Orbits in Semisimple Lie Algebras, Van NostrandReinhold, New York, 1993. Zbl0972.17008MR1251060
- [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. Zbl0786.22023MR1216434
- [19] R. Goodman and N. Wallach: Whittaker vectors and conical vectors, J. Funct. Anal.39 (1980) 199-279. Zbl0475.22010MR597811
- [20] H. Hecht and W. Schmid: Characters, asymptotics and n-homology of Harish-Chandra modules, Acta Math.151 (1983) 49-151. Zbl0523.22013MR716371
- [21] R. Irving: Projective modules in the category Os: Self-duality, Trans. Amer. Math. Soc.291 (1985) 701—732. Zbl0594.17005
- [22] B. Kostant: On Whittaker vectors and representation theory, Invent. Math.48 (1978) 101-184. Zbl0405.22013MR507800
- [23] G. Lusztig: A class of irreducible representations of a Weyl group II, Indag. Math.44 (1982) 219-226. Zbl0511.20034MR662657
- [24] G. Lusztig and D. Vogan: Singularities of closures of K-orbits on flag manifolds, Inv. Math.71 (1983) 365-379. Zbl0544.14035MR689649
- [25] H. Matumoto: Whittaker vectors and associated varieties, Invent. Math.89 (1987) 219-224. Zbl0633.17006MR892192
- [26] H. Matumoto: Whittaker vectors and the Goodman—Wallach operators, Acta Math.161 (1988) 183-241. Zbl0723.22019
- [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. Zbl0760.22017
- [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. Zbl0797.22005
- [29] R. Proctor: Classical Bruhat orders and lexicographic shellability, J. Algebra77 (1982) 104-126. Zbl0486.06002MR665167
- [30] W. Soergel: Equivalences de certaines de g-modules, C.R. Acad. Sci. Paris303 (1986). Zbl0623.17005MR872544
- [31] D. Vogan: Gelfand-Kirillov dimensions for Harish-Chandra modules, Invent. Math.48 (1978) 75-98. Zbl0389.17002MR506503
- [32] D. Vogan: Representations of real reductive Lie groups, Birkhäuser, Boston, 1981. Zbl0469.22012MR632407
- [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. Zbl0505.22016MR689650
- [34] D. Vogan: Irreducible characters of semisimple Lie groups IV: character multiplicity duality, Duke Math. J.49 (1982) 943-1073. Zbl0536.22022MR683010
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.