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 unitary dual of p-adic $ SO(5)$


Author: Ivan Matic
Journal: Proc. Amer. Math. Soc. 138 (2010), 759-767
MSC (2000): Primary 22E50, 20G05
DOI: https://doi.org/10.1090/S0002-9939-09-10065-5
Published electronically: September 28, 2009
MathSciNet review: 2557193
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ F$ be a $ p$-adic field of characteristic zero. We investigate the composition series of the parabolically induced representations of $ SO(5,F)$ and determine the non-cuspidal part of the unitary dual of $ SO(5,F)$.


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

  • 1. A.-M. Aubert, Dualité dans le groupe de Grothendieck de la catégorie des représentations lisses de longueur finie d'un groupe réductif $ p$-adique, Trans. Amer. Math. Soc., 347 (1995), pp. 2179-2189. MR 1285969 (95i:22025)
  • 2. -, Erratum: ``Duality in the Grothendieck group of the category of finite-length smooth representations of a $ p$-adic reductive group'' [Trans. Amer. Math. Soc. 347 (1995), no. 6, 2179-2189, MR 1285969 (95i:22025)]; Trans. Amer. Math. Soc., 348 (1996), pp. 4687-4690. MR 1390967 (97c:22019)
  • 3. W. Casselman, A new nonunitarity argument for $ p$-adic representations, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 28 (1981), pp. 907-928 (1982). MR 656064 (84e:22018)
  • 4. M. Hanzer and G. Muić, On an algebraic approach to the Zelevinsky classification for classical $ p$-adic groups, J. Algebra, 320 (2008), pp. 3206-3231. MR 2450724
  • 5. C. Jantzen, Degenerate principal series for orthogonal groups, J. Reine Angew. Math., 441 (1993), pp. 61-98. MR 1228612 (94f:22022)
  • 6. C. D. Keys, On the decomposition of reducible principal series representations of $ p$-adic Chevalley groups, Pacific J. Math., 101 (1982), pp. 351-388. MR 675406 (84d:22032)
  • 7. D. Miličić, On $ C\sp{\ast} $-algebras with bounded trace, Glasnik Mat. Ser. III, 8(28) (1973), pp. 7-22. MR 0324429 (48:2781)
  • 8. G. Muić, The unitary dual of $ p$-adic $ G\sb 2$, Duke Math. J., 90 (1997), pp. 465-493. MR 1480543 (98k:22073)
  • 9. -, Composition series of generalized principal series; the case of strongly positive discrete series, Israel J. Math., 140 (2004), pp. 157-202. MR 2054843 (2005e:22018)
  • 10. -, A geometric construction of intertwining operators for reductive $ p$-adic groups, Manuscripta Math., 125 (2008), pp. 241-272. MR 2373084
  • 11. P. J. Sally, Jr. and M. Tadić, Induced representations and classifications for GSp$ (2,F)$ and Sp$ (2,F)$, Mém. Soc. Math. France (N.S.), No. 52 (1993), pp. 75-133. MR 1212952 (94e:22030)
  • 12. F. Shahidi, A proof of Langlands' conjecture on Plancherel measures; complementary series for $ p$-adic groups, Ann. of Math. (2), 132 (1990), pp. 273-330. MR 1070599 (91m:11095)
  • 13. T. A. Springer, Reductive groups, in Automorphic forms, representations and $ L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 1, Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 3-27. MR 546587 (80h:20062)
  • 14. M. Tadić, An external approach to unitary representations, Bull. Amer. Math. Soc. (N.S.), 28 (1993), pp. 215-252. MR 1181278 (93g:22020)
  • 15. -, Representations of $ p$-adic symplectic groups, Compositio Math., 90 (1994), pp. 123-181. MR 1266251 (95a:22025)
  • 16. -, On reducibility of parabolic induction, Israel J. Math., 107 (1998), pp. 29-91. MR 1658535 (2001d:22012)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 22E50, 20G05

Retrieve articles in all journals with MSC (2000): 22E50, 20G05


Additional Information

Ivan Matic
Affiliation: Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, Osijek, Croatia
Email: imatic@mathos.hr

DOI: https://doi.org/10.1090/S0002-9939-09-10065-5
Received by editor(s): February 6, 2009
Received by editor(s) in revised form: May 14, 2009, and May 31, 2009
Published electronically: September 28, 2009
Communicated by: Gail R. Letzter
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society