Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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


Authors: Dubravka Ban and Chris Jantzen
Journal: Proc. Amer. Math. Soc. 131 (2003), 3297-3304
MSC (2000): Primary 22E50
DOI: https://doi.org/10.1090/S0002-9939-03-07145-4
Published electronically: May 12, 2003
MathSciNet review: 1992872
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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


References [Enhancements On Off] (What's this?)

  • [B-J1] D. Ban and C. Jantzen, The Langlands classification for non-connected $p$-adic groups, Israel Journal of Mathematics, 126 (2001), 239-261. MR 2002i:22018
  • [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, Annales Scientifiques de l'École Normale Supérieure 10 (1977), 441-472. MR 58:28310
  • [B-W] A. Borel and N. Wallach, Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups - 2nd ed., Mathematical Surveys and Monographs 67 (2000). MR 2000j:22015
  • [G-K] S. Gelbart and A. Knapp, $L$-indistinguishability and $R$ groups for the special linear group, Advances in Mathematics 43 (1982), 101-121. MR 83j:22009
  • [G-H] D. Goldberg and R. Herb, Some results on the admissible representations of non-connected reductive $p$-adic groups, Annales Scientifiques de l'École Normale Supérieure 30 (1997), 97-146. MR 98b:22033
  • [H] Harish-Chandra, Harmonic analysis on reductive $p$-adic groups, Proceedings of Symposia in Pure Mathematics 26 (1974), 167-192. MR 49:5238
  • [J] C. Jantzen, Duality and supports of induced representations for even-orthogonal groups, preprint.
  • [M] Z. Magyar, Langlands classification for real Lie groups with reductive Lie algebra, Acta Applicandae Mathematicae 37 (1994), 267-309. MR 96i:22035
  • [L] R. Langlands, On the classification of irreducible representations of real algebraic groups, Representation Theory and Harmonic Analysis on Semisimple Lie Groups, editors Paul Sally, Jr. and David Vogan, Mathematical Surveys and Monographs, AMS, vol. 31, 1989, pp.101-170. MR 91e:22017
  • [S] A. Silberger, The Langlands quotient theorem for $p$-adic groups, Mathematische Annalen 236 (1978), 95-104. MR 58:22413

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 22E50

Retrieve articles in all journals with MSC (2000): 22E50


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

American Mathematical Society