-groups and elliptic representations for unitary groups

Author:
David Goldberg

Journal:
Proc. Amer. Math. Soc. **123** (1995), 1267-1276

MSC:
Primary 22E35; Secondary 22D30, 22E50

DOI:
https://doi.org/10.1090/S0002-9939-1995-1224616-6

MathSciNet review:
1224616

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We determine the reducibility and number of components of any representation of a quasi-split unitary group which is parabolically induced from a discrete series representation. The *R*-groups are computed explicitly, in terms of reducibility for maximal parabolics. This gives a description of the elliptic representations.

**[1]**J. Arthur,*On elliptic temptered characters*, Acta Math.**171**(1993), 73-138. MR**1237898 (94i:22038)****[2]**I. N. Bernstein and A. V. Zelevinsky,*Induced representations of reductive p-adic groups*. I, Ann. Sci. École Norm. Sup. (4)**10**(1977), 441-472. MR**0579172 (58:28310)****[3]**D. Goldberg,*R-groups and elliptic representations for*, Pacific J. Math.**165**(1994), 77-92. MR**1285565 (95h:22020)****[4]**-,*Reducibility of induced representations for**and*, Amer. J. Math.**484**(1994), 65-95.**[5]**-,*Some results on reducibility for unitary groups and local Asai L-functions*, J. Reine Angew. Math.**448**(1994), 65-95. MR**1266747 (95g:22031)****[6]**Harish-Chandra,*Harmonic analysis on reductive p-adic groups*, Proc. Sympos. Pure Math., vol. 26, Amer. Math. Soc., Providence, RI, 1973, pp. 167-192. MR**0340486 (49:5238)****[7]**R. A. Herb,*Elliptic representations for**and*, Pacific J. Math.**161**(1993), 347-358. MR**1242203 (94i:22040)****[8]**H. Jacquet,*Generic representations*, Non Commutative Harmonic Analysis, Lecture Notes in Math., vol. 587, Springer-Verlag, New York, Heidelberg, and Berlin, 1977, pp. 91-101. MR**0499005 (58:16985)****[9]**C. D. Keys,*On the decomposition of reducible principal series representations of p-adic Chevalley groups*, Pacific J. Math.**101**(1982), 351-388. MR**675406 (84d:22032)****[10]**-,*L-indistinguishability and R-groups for quasi split groups*:*unitary groups in even dimension*, Ann. Sci. École Norm. Sup. (4)**20**(1987), 31-64. MR**892141 (88m:22042)****[11]**A. W. Knapp and E. M. Stein,*Irreducibility theorems for the principal series*, Conference on Harmonic Analysis, Lecture Notes in Math., vol. 266, Springer-Verlag, New York, Heidelberg, and Berlin, 1972, pp. 197-214. MR**0422512 (54:10499)****[12]**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. USSR-Sb**22**(1974), 217-254.**[13]**F. Shahidi,*The notion of norm and the representation theory of orthogonal groups*, Invent. Math, (to appear). MR**1309970 (96e:22034)****[14]**-,*On certain L-functions*, Amer. J. Math.**103**(1981), 297-355. MR**610479 (82i:10030)****[15]**A. J. Silberger,*The Knapp-Stein dimension theorem for p-adic groups*, Proc. Amer. Math. Soc.**68**(1978), 243-246;*Correction*, Proc. Amer. Math. Soc.**76**(1979), 169-170. MR**0492091 (58:11245)****[16]**-,*Introduction to harmonic anaysis on reductive p-adic groups*, Math. Notes, vol. 23, Princeton Univ. Press, Princeton, NJ, 1979. MR**544991 (81m:22025)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
22E35,
22D30,
22E50

Retrieve articles in all journals with MSC: 22E35, 22D30, 22E50

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1995-1224616-6

Article copyright:
© Copyright 1995
American Mathematical Society