groups and elliptic representations for unitary groups
Author:
David Goldberg
Journal:
Proc. Amer. Math. Soc. 123 (1995), 12671276
MSC:
Primary 22E35; Secondary 22D30, 22E50
MathSciNet review:
1224616
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Abstract: We determine the reducibility and number of components of any representation of a quasisplit unitary group which is parabolically induced from a discrete series representation. The Rgroups are computed explicitly, in terms of reducibility for maximal parabolics. This gives a description of the elliptic representations.
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 [5]
 , Some results on reducibility for unitary groups and local Asai Lfunctions, J. Reine Angew. Math. 448 (1994), 6595. MR 1266747 (95g:22031)
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 HarishChandra, Harmonic analysis on reductive padic groups, Proc. Sympos. Pure Math., vol. 26, Amer. Math. Soc., Providence, RI, 1973, pp. 167192. MR 0340486 (49:5238)
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 R. A. Herb, Elliptic representations for and , Pacific J. Math. 161 (1993), 347358. MR 1242203 (94i:22040)
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 H. Jacquet, Generic representations, Non Commutative Harmonic Analysis, Lecture Notes in Math., vol. 587, SpringerVerlag, New York, Heidelberg, and Berlin, 1977, pp. 91101. MR 0499005 (58:16985)
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 C. D. Keys, On the decomposition of reducible principal series representations of padic Chevalley groups, Pacific J. Math. 101 (1982), 351388. MR 675406 (84d:22032)
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 , Lindistinguishability and Rgroups for quasi split groups: unitary groups in even dimension, Ann. Sci. École Norm. Sup. (4) 20 (1987), 3164. MR 892141 (88m:22042)
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 A. W. Knapp and E. M. Stein, Irreducibility theorems for the principal series, Conference on Harmonic Analysis, Lecture Notes in Math., vol. 266, SpringerVerlag, New York, Heidelberg, and Berlin, 1972, pp. 197214. MR 0422512 (54:10499)
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 G. I. Ol'sanskii, Intertwining operators and complementary series in the class of representations induced from parabolic subgroups of the genreal linear group over a locally compact division algebra, Math. USSRSb 22 (1974), 217254.
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 F. Shahidi, The notion of norm and the representation theory of orthogonal groups, Invent. Math, (to appear). MR 1309970 (96e:22034)
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 , On certain Lfunctions, Amer. J. Math. 103 (1981), 297355. MR 610479 (82i:10030)
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 A. J. Silberger, The KnappStein dimension theorem for padic groups, Proc. Amer. Math. Soc. 68 (1978), 243246; Correction, Proc. Amer. Math. Soc. 76 (1979), 169170. MR 0492091 (58:11245)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199512246166
PII:
S 00029939(1995)12246166
Article copyright:
© Copyright 1995
American Mathematical Society
