Duke Mathematical Journal

Depth preservation in local theta correspondence

Shu-Yen Pan

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Abstract

In this paper, we prove that the depths of irreducible admissible representations are preserved by the local theta correspondence for any type I reductive dual pairs over a nonarchimedean local field.

Article information

Source
Duke Math. J. Volume 113, Number 3 (2002), 531-592.

Dates
First available in Project Euclid: 18 June 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1087575316

Digital Object Identifier
doi:10.1215/S0012-7094-02-11334-9

Mathematical Reviews number (MathSciNet)
MR1909608

Zentralblatt MATH identifier
1011.22009

Subjects
Primary: 22E50: Representations of Lie and linear algebraic groups over local fields [See also 20G05]
Secondary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields

Citation

Pan, Shu-Yen. Depth preservation in local theta correspondence. Duke Math. J. 113 (2002), no. 3, 531--592. doi:10.1215/S0012-7094-02-11334-9. http://projecteuclid.org/euclid.dmj/1087575316.


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References

  • A.-M. Aubert, Correspondance de Howe et sous-groupes parahoriques, J. Reine Angew. Math. 392 (1988), 176--186.
  • F. Bruhat and J. Tits, Schémas en groupes et immeubles des groupes classiques sur un corps local, II: Groupes unitaires, Bull. Soc. Math. France 115 (1987), 141--195.
  • R. Howe, ``$\theta$-series and invariant theory'' in Automorphic Forms, Representations and L-functions (Corvallis, Ore., 1977), Part I, Proc. Sympos. Pure Math. 33, Amer. Math. Soc., Providence, 1979, 275--285.
  • N. Iwahori and H. Matsumoto, On some Bruhat decomposition and the structure of the Hecke ring of $\mathfrakp$-adic Chevalley groups, Inst. Hautes Études Sci. Publ. Math. 25 (1965), 5--48.
  • S. Kudla, On the local theta-correspondence, Invent. Math. 83 (1986), 229--255.
  • --. --. --. --., Splitting metaplectic covers of dual reductive pairs, Israel J. Math. 87 (1994), 361--401.
  • C. Mœglin, M.-F. Vignéras, and J.-L. Waldspurger, Correspondances de Howe sur un corps p-adique, Lecture Notes in Math. 1291, Springer, Berlin, 1987.
  • A. Moy and G. Prasad, Unrefined minimal $K$-types for $p$-adic groups, Invent. Math. 116 (1994), 393--408.
  • --. --. --. --., Jacquet functors and unrefined minimal $K$-types, Comment Math. Helv. 71 (1996), 98--121.
  • S.-Y. Pan, Splittings of the metaplectic covers of some reductive dual pairs, Pacific J. Math. 199 (2001), 163--226. \CMP1 847 153
  • --------, Local theta correspondence of representations of depth zero and theta dichotomy, to appear in J. Math. Soc. Japan.
  • D. Prasad, ``Weil representation, Howe duality, and the theta correspondence'' in Theta Functions: From the Classical to the Modern, CRM Proc. Lecture Notes 1, Amer. Math. Soc., Providence, 1993, 105--127.
  • J.-L. Waldspurger, ``Démonstration d'une conjecture de dualité de Howe dans le cas $p$-adique, $p\neq 2$'' in Festschrift in Honor of I. I. Piatetski-Shapiro, on the Occasion of His Sixtieth Birthday (Ramat Aviv, Israel, 1989), Part 1, Israel Math. Conf. Proc. 2, Weizmann, Jerusalem, 1990, 267--324.
  • J.-K. Yu, Descent mapping in Bruhat-Tits theory, preprint, 1998.