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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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The Bernstein center in terms of invariant locally integrable functions
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by Allen Moy and Marko Tadić PDF
Represent. Theory 6 (2002), 313-329 Request permission

Abstract:

We give a description of the Bernstein center of a reductive $p$-adic group $G$ in terms of invariant locally integrable functions and compute a basis of these functions for the group $SL(2)$.
References
  • 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
  • J. Bernstein, P. Deligne, and D. Kazhdan, Trace Paley-Wiener theorem for reductive $p$-adic groups, J. Analyse Math. 47 (1986), 180–192. MR 874050, DOI 10.1007/BF02792538
  • G. van Dijk, Computation of certain induced characters of ${\mathfrak {p}}$-adic groups, Math. Ann. 199 (1972), 229–240. MR 338277, DOI 10.1007/BF01429876
  • 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, DOI 10.1090/pspum/026/0340486
  • 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 Papers in Pure Appl. Math., No. 48, Queen’s Univ., Kingston, Ont., 1978, pp. 281–347. MR 0579175
  • David Kazhdan, Cuspidal geometry of $p$-adic groups, J. Analyse Math. 47 (1986), 1–36. MR 874042, DOI 10.1007/BF02792530
  • Marko Tadić, Geometry of dual spaces of reductive groups (non-Archimedean case), J. Analyse Math. 51 (1988), 139–181. MR 963153, DOI 10.1007/BF02791122
  • [W]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
  • MR Author ID: 127665
  • Email: moy@math.lsa.umich.edu, amoy@math.ust.hk
  • Marko Tadić
  • Affiliation: Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia
  • ORCID: 0000-0002-6087-3765
  • Email: tadic@math.hr
  • Received by editor(s): February 7, 2002
  • Received by editor(s) in revised form: August 27, 2002
  • Published electronically: 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
  • © Copyright 2002 American Mathematical Society
  • Journal: Represent. Theory 6 (2002), 313-329
  • MSC (2000): Primary 22E50, 22E35
  • DOI: https://doi.org/10.1090/S1088-4165-02-00181-4
  • MathSciNet review: 1979109