The Langlands classification for non-connected -adic groups II: Multiplicity one

Authors:
Dubravka Ban and Chris Jantzen

Journal:
Proc. Amer. Math. Soc. **131** (2003), 3297-3304

MSC (2000):
Primary 22E50

Published electronically:
May 12, 2003

MathSciNet review:
1992872

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Abstract | References | Similar Articles | Additional Information

Abstract: For a non-connected reductive -adic group, we prove that the Langlands subrepresentation appears with multiplicity one in the representation parabolically induced from the corresponding Langlands data.

**[B-J1]**Dubravka Ban and Chris Jantzen,*The Langlands classification for non-connected 𝑝-adic groups*, Israel J. Math.**126**(2001), 239–261. MR**1882038**, 10.1007/BF02784155**[B-J2]**D. Ban and C. Jantzen,*Degenerate principal series for even-orthogonal groups*, preprint.**[B-Z]**I. N. Bernstein and A. V. Zelevinsky,*Induced representations of reductive 𝔭-adic groups. I*, Ann. Sci. École Norm. Sup. (4)**10**(1977), no. 4, 441–472. MR**0579172****[B-W]**A. Borel and N. Wallach,*Continuous cohomology, discrete subgroups, and representations of reductive groups*, 2nd ed., Mathematical Surveys and Monographs, vol. 67, American Mathematical Society, Providence, RI, 2000. MR**1721403****[G-K]**S. S. Gelbart and A. W. Knapp,*𝐿-indistinguishability and 𝑅 groups for the special linear group*, Adv. in Math.**43**(1982), no. 2, 101–121. MR**644669**, 10.1016/0001-8708(82)90030-5**[G-H]**David Goldberg and Rebecca Herb,*Some results on the admissible representations of non-connected reductive 𝑝-adic groups*, Ann. Sci. École Norm. Sup. (4)**30**(1997), no. 1, 97–146. MR**1422314**, 10.1016/S0012-9593(97)89916-8**[H]**Harish-Chandra,*Harmonic analysis on reductive 𝑝-adic groups*, Harmonic analysis on homogeneous spaces (Proc. Sympos. Pure Math., Vol. XXVI, Williams Coll., Williamstown, Mass., 1972) Amer. Math. Soc., Providence, R.I., 1973, pp. 167–192. MR**0340486****[J]**C. Jantzen,*Duality and supports of induced representations for even-orthogonal groups*, preprint.**[M]**Zoltán Magyar,*Langlands classification for real Lie groups with reductive Lie algebra*, Acta Appl. Math.**37**(1994), no. 3, 267–309. MR**1326628**, 10.1007/BF00992639**[L]**R. P. Langlands,*On the classification of irreducible representations of real algebraic groups*, Representation theory and harmonic analysis on semisimple Lie groups, Math. Surveys Monogr., vol. 31, Amer. Math. Soc., Providence, RI, 1989, pp. 101–170. MR**1011897**, 10.1090/surv/031/03**[S]**Allan J. Silberger,*The Langlands quotient theorem for 𝑝-adic groups*, Math. Ann.**236**(1978), no. 2, 95–104. MR**0507262**

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Additional Information

**Dubravka Ban**

Affiliation:
Department of Mathematics, Southern Illinois University, Carbondale, Illinois 62901

Email:
dban@math.siu.edu

**Chris Jantzen**

Affiliation:
Department of Mathematics, East Carolina University, Greenville, North Carolina 27858

Email:
jantzenc@mail.ecu.edu

DOI:
https://doi.org/10.1090/S0002-9939-03-07145-4

Received by editor(s):
May 16, 2002

Published electronically:
May 12, 2003

Communicated by:
Rebecca Herb

Article copyright:
© Copyright 2003
American Mathematical Society