Glasnik Matematicki, Vol. 48, No. 2 (2013), 313-334.
THE LANGLANDS QUOTIENT THEOREM FOR FINITE CENTRAL EXTENSIONS OF p-ADIC GROUPS
Dubravka Ban and Chris Jantzen
Department of Mathematics,
Southern Illinois University, Carbondale, IL 62901 , USA
e-mail: dban@math.siu.edu
Department of Mathematics, East Carolina University,
Greenville, NC 27858, USA
e-mail: jantzenc@ecu.edu
Abstract. In this paper, we prove the Langlands quotient theorem in the context of finite central extensions of connected, reductive p-adic groups.
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.48.2.07
References:
-
J. Arthur,
An introduction to the trace formula,
in Harmonic analysis, the trace formula, and Shimura varieties,
Clay Math. Proc. 4, Amer. Math. Soc., Providence, RI, 2005, 1-263.
MathSciNet
-
D. Ban and C. Jantzen,
Jacquet modules and the Langlands classification,
Michigan Math. J. 56 (2008), 637-653.
MathSciNet
CrossRef
-
J. Bernstein,
Representations of p-adic groups,
Lectures, Harvard University, Fall 1992.
-
I. Bernstein and A. Zelevinsky,
Induced representations of reductive p-adic groups I,
Ann. Sci. École Norm. Sup. 10 (1977), 441-472.
MathSciNet
CrossRef
-
A. Borel, Liner Algebraic Groups, 2nd Edition, Springer-Verlag, New York, 1991.
MathSciNet
-
A. Borel and N. Wallach,
Continuous cohomology, discrete subgroups, and representations
of reductive groups, Princeton University Press, Princeton, 1980.
MathSciNet
-
N. Bourbaki,
Lie Groups and Lie Algebras (Chapters 4-6),
Springer-Verlag, Berlin, 2002.
MathSciNet
-
J.-L. Brylinski and P. Deligne,
Central extensions of reductive groups by K2,
Publ. Math. Inst. Hautes Études Sci. 94 (2001), 5-85.
MathSciNet
CrossRef
-
W. Casselman,
Introduction to the theory of admissible representations of p-adic
reductive groups,
preprint.
-
S. Evens, The Langlands classification for graded Hecke algebras,
Proc. Amer. Math. Soc. 124 (1996), 1285-1290.
MathSciNet
CrossRef
-
R. Gustafson,
The degenerate principal series for Sp(2n),
Mem. Amer. Math. Soc.
33 (1981).
MathSciNet
CrossRef
-
M. Hanzer and G. Muić,
Parabolic induction and Jacquet functors for mateplectic groups,
J. Algebra 323 (2010), 241-260.
MathSciNet
CrossRef
-
Harish-Chandra, Harmonic analysis on reductive p-adic
groups, Proceedings of Symposia in Pure Mathematics 26 (1973),
167-192.
MathSciNet
CrossRef
-
C. Jantzen,
Some remarks on degenerate principal series,
Pacific J. Math. 186 (1998), 67-87.
MathSciNet
CrossRef
-
D. Kazhdan and S. Kazhdan,
Metaplectic forms,
Inst. Hautes Études Sci. Publ. Math. 59 (1984), 35-142.
MathSciNet
CrossRef
-
A. Knapp,
Representation Theory of Semisimple Groups; An Overview Based on Examples,
Princeton University Press, Princeton, 1986.
MathSciNet
-
T. Konno,
A note on the Langlands classification and irreducibility of induced representations of p-adic groups,
Kyushu J. Math. 57 (2003), 383-409.
MathSciNet
CrossRef
-
S. Kudla,
On the local theta-correspondence,
Invent. Math. 83 (1986), 229-255.
MathSciNet
CrossRef
-
S. Lang, Algebra, 3rd revised ed., New York, Springer, 2002.
MathSciNet
-
R. Langlands,
On the classification of irreducible representations of real algebraic groups,
in Representation theory and harmonic analysis on semisimple Lie groups, Amer. Math. Soc., Providence, 1989, 101-170.
MathSciNet
-
C. Mœglin and J.-L. Waldspurger,
Spectral Decomposition and Eisenstein Series, Cambridge University Press, Cambridge, 1995.
MathSciNet
-
A. Silberger,
The Langlands quotient theorem for p-adic groups,
Math. Ann. 236 (1978), 95-104.
MathSciNet
CrossRef
-
J.-L. Waldspurger,
La formule de Plancherel pour les groupes p-adiques (d'après Harish-Chandra),
J. Inst. Math. Jussieu 2 (2003), 235-333.
MathSciNet
CrossRef
-
M. Weissman,
Metaplectic tori over local fields,
Pacific J. Math.
241 (2009), 169-200.
MathSciNet
CrossRef
Glasnik Matematicki Home Page