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The Bernstein center in terms of invariant locally integrable functions
Authors:
Allen Moy and Marko Tadic
Journal:
Represent. Theory 6 (2002), 313-329
MSC (2000):
Primary 22E50, 22E35
Posted:
November 19, 2002
Erratum:
Represent. Theory 9 (2005), 455-456.
MathSciNet review:
1979109
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Abstract: We give a description of the Bernstein center of a reductive  -adic group  in terms of invariant locally integrable functions and compute a basis of these functions for the group  .
- [BD]
J.
N. Bernstein, Le “centre” de Bernstein,
Representations of reductive groups over a local field, Travaux en Cours,
Hermann, Paris, 1984, pp. 1–32 (French). Edited by P. Deligne.
MR 771671
(86e:22028)
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Bernstein, P.
Deligne, and D.
Kazhdan, Trace Paley-Wiener theorem for reductive 𝑝-adic
groups, J. Analyse Math. 47 (1986), 180–192. MR 874050
(88g:22016), http://dx.doi.org/10.1007/BF02792538
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G.
van Dijk, Computation of certain induced characters of
𝔭-adic groups, Math. Ann. 199 (1972),
229–240. MR 0338277
(49 #3043)
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Harish-Chandra,
Harmonic analysis on reductive 𝑝-adic groups, Harmonic
analysis on homogeneous spaces (Proc. Sympos. Pure Math., Vol. XXVI,
Williams Coll., Williamstown, Mass., 1972), Amer. Math. Soc., Providence,
R.I., 1973, pp. 167–192. MR 0340486
(49 #5238)
- [HC2]
Harish-Chandra,
Admissible invariant distributions on reductive 𝑝-adic
groups, Lie theories and their applications (Proc. Ann. Sem. Canad.
Math. Congr., Queen’s Univ., Kingston, Ont., 1977), Queen’s
Univ., Kingston, Ont., 1978, pp. 281–347. Queen’s Papers
in Pure Appl. Math., No. 48. MR 0579175
(58 #28313)
- [K]
David
Kazhdan, Cuspidal geometry of 𝑝-adic groups, J.
Analyse Math. 47 (1986), 1–36. MR 874042
(88g:22017), http://dx.doi.org/10.1007/BF02792530
- [T]
Marko
Tadić, Geometry of dual spaces of reductive groups
(non-Archimedean case), J. Analyse Math. 51 (1988),
139–181. MR
963153 (90c:22057), http://dx.doi.org/10.1007/BF02791122
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Waldspurger, J.-L., La formule de Plancherel pour les groupes p-adiques, preprint.
- [BD]
- Bernstein, J. (edited by Deligne, P.), Le ``centre" de Bernstein, in ``Représentations des Groupes Réductifs sur un Corps Local" written by J.-N. Bernstein, P. Deligne, D. Kazhdan, M.-F. and Vignéras,, Hermann, Paris, 1984. MR 86e:22028
- [BDK]
- Bernstein, J., Deligne, P. and Kazhdan, D., Trace Paley-Wiener theorem for reductive
 -adic groups, J. Analyse Math 47 (1986), 180-192. MR 88g:22016
- [vD]
- Dijk, G. van, Computation of certain induced characters of
 -adic groups, Math. Ann. 199 (1972), 229-240. MR 49:3043
- [HC1]
- Harish-Chandra, Harmonic analysis on reductive
 -adic groups, Symp. Pure Math. 26,, Amer. Math. Soc., Providence, Rhone Island, 1973, pp. 167-192. MR 49:5238
- [HC2]
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 -adic groups, Lie theories and their applications (Proc. Ann. Sem. Canad. Math. Congr., Queen's Univ., Kingston, Ont., 1977). Queen's Papers in Pure Appl. Math., No. 48, Queen's Univ., Kingston, Ont., 1978, pp. 281-347. MR 58:28313
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- Kazhdan, D., Cuspidal geometry of
 -adic groups, J. Analyse Math. 47 (1986), 1-36. MR 88g:22017
- [T]
- Tadic, M., Geometry of dual spaces of reductive groups (non-archimedean case), J. Analyse Math. 51 (1988), 139-181. MR 90c:22057
- [W]
- Waldspurger, J.-L., La formule de Plancherel pour les groupes p-adiques, preprint.
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Additional Information
Allen Moy
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109;
Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong, SAR
Email:
moy@math.lsa.umich.edu, amoy@math.ust.hk
Marko Tadic
Affiliation:
Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia
Email:
tadic@math.hr
DOI:
http://dx.doi.org/10.1090/S1088-4165-02-00181-4
PII:
S 1088-4165(02)00181-4
Received by editor(s):
February 7, 2002
Received by editor(s) in revised form:
August 27, 2002
Posted:
November 19, 2002
Additional Notes:
The first and second authors acknowledge partial support from the National Science Foundation grants DMS-9801264 and DMS-0100413
The second author acknowledges partial support from the Croatian Ministry of Science and Technology grant #37001
Article copyright:
© Copyright 2002 American Mathematical Society
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