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Theta-lifting and geometric quantization for GL(n, ?) |
Mingjing ZHANG( ) |
| School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China |
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Abstract In this paper, we verify Vogan’s conjecture on quantization in the representation theory for G = GL(n, ?). Also we get some relationship between the induction of orbits and Howe’s θ-lifting of unitary representations.
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| Keywords
Vogan’s conjecture on quantization
induced orbits
unitary representations
theta-lifting
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Corresponding Author(s):
ZHANG Mingjing,Email:0310030@mail.nankai.edu.cn
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Issue Date: 01 August 2012
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| 1 |
Adams J, Barbasch D. Reductive dual pair correspondence for complex groups. J Funct Anal , 1995, 132: 1-42
doi: 10.1006/jfan.1995.1099
|
| 2 |
Adams J, Huang J S, Vogan D. Functions on the model orbits in E8. Represent Theory , 1998, 2: 224-263
doi: 10.1090/S1088-4165-98-00048-X
|
| 3 |
Collingwood D, McGovern W. Nilpotent Orbits in Semisimple Lie Algebras. New York: Chapman and Hall, 1993
|
| 4 |
Howe R. θ-series and invariant theory. Proc Sympos Pure Math , 1979, 33(1): 275-285
|
| 5 |
Howe R. Transcending classical invariant theory. J Amer Math Soc , 1989, 2: 535-552
doi: 10.1090/S0894-0347-1989-0985172-6
|
| 6 |
Kostant B. Quantization and unitary representations. In: Taam C, ed. Lectures in Modern Analysis and Applications. Lecture Notes in Mathematics, Vol 170 . Berlin-Heidelberg-New York: Springer-Verlag, 1970, 87-207
|
| 7 |
Lusztig G, Spaltenstein N. Induced unipotent classes. J Lond Math Soc , 1979, 19: 41-52
doi: 10.1112/jlms/s2-19.1.41
|
| 8 |
Namikawa Y. Induced nilpotent orbits and birational geometry. Adv Math , 2009, 222: 547-564
doi: 10.1016/j.aim.2009.05.001
|
| 9 |
Torasso P. Quantification géométrique, opérateurs d’entrelacement et représentations unitarires de SL~3(?). Acta Math , 1983, 150: 153-242
doi: 10.1007/BF02392971
|
| 10 |
Vogan D. Unitary Representations of Reductive Lie Groups. Annals of Mathematics Studies . Princeton: Princeton University Press, 1987
|
| 11 |
Vogan D. Associated varieties and unipotent representations. In: Barker W, Sally P, eds. Harmonic Analysis on Reductive Groups . Boston-Basel-Berlin: Birkh?user, 1991, 315-388
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