Glasnik Matematicki, Vol. 51, No. 1 (2016), 153-163.
THE LANGLANDS QUOTIENT THEOREM FOR FINITE CENTRAL EXTENSIONS OF P-ADIC GROUPS II: INTERTWINING OPERATORS AND DUALITY
Dubravka Ban and Chris Jantzen
Department of Mathematics,
Southern Illinois University, Carbondale, IL 62901 , USA
e-mail: dban@siu.edu
Department of Mathematics, East Carolina University,
Greenville, NC 27858, USA
e-mail: jantzenc@ecu.edu
Abstract.
In this paper, we prove that the Langlands quotient may be realized as the image of a standard intertwining operator in the context of finite central extensions of connected,
reductive p-adic groups. We also verify that the duality of Aubert and Schneider-Stuhler holds in this context
2010 Mathematics Subject Classification.
22E50, 11F70.
Key words and phrases. Metaplectic groups; Langlands quotient theorem; p-adic groups.
Full text (PDF) (free access)
DOI: 10.3336/gm.51.1.09
References:
-
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), 2179-2189.
MathSciNet
CrossRef
-
A.-M. Aubert,
Erratum:``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. 348 (1996), 4687-4690.
MathSciNet
CrossRef
-
D. Ban and C. Jantzen,
The Langlands quotient theorem for finite central extensions of p-adic groups,
Glas. Mat. Ser. III 48(68) (2013), 313-334.
MathSciNet
CrossRef
-
J. Bernstein,
Representations of p-adic groups,
Lectures, Harvard University, Fall 1992.
-
J. Bernstein, P. Deligne and D. Kazhdan,
Trace Paley-Wiener theorem for reductive p-adic groups,
J. Analyse Math. 47 (1986), 180-192.
MathSciNet
CrossRef
-
I. Bernstein and A. Zelevinsky,
Induced representations of reductive p-adic groups I,
Ann. Sci. École Norm. Sup. 10
(1977), 441-472.
MathSciNet
CrossRef
-
W. Casselman,
Introduction to the theory of admissible representations of p-adic
reductive groups,
preprint.
-
Harish-Chandra,
Harmonic analysis on reductive p-adic groups,
Proceedings of Symposia in Pure Mathematics 26, Amer. Math. Soc., R.I., 1973,
167-192.
MathSciNet
-
C. Jantzen,
Some remarks on degenerate principal series,
Pacific J. Math. 186 (1998), 67-87.
MathSciNet
CrossRef
-
W. Li,
La formule des traces pour les revêtements de groupes réductifs connexes. II. Analyse harmonique locale.,
Ann. Sci. Éc. Norm. Supér. (4) 45 (2012), 787-859.
MathSciNet
-
C. Mœglin and J.-L. Waldspurger,
Spectral decomposition and Eisenstein series, Cambridge University Press, Cambridge, 1995.
MathSciNet
CrossRef
-
P. Schneider and U. Stuhler,
Representation theory and sheaves on the Bruhat-Tits building,
Inst. Hautes Études Sci. Publ. Math. No. 85 (1997), 97-191.
MathSciNet
CrossRef
link
-
A. Silberger,
Introduction to harmonic analysis on reductive p-adic groups,
Princeton University Press, Princeton, 1979.
MathSciNet
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