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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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Conjugacy class asymptotics, orbital integrals, and the Bernstein center: the case of $SL(2)$
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by Allen Moy and Marko Tadić PDF
Represent. Theory 9 (2005), 327-353 Request permission

Abstract:

The Bernstein center of a reductive p-adic group is the algebra of conjugation invariant distributions on the group which are essentially compact, i.e., invariant distributions whose convolution against a locally constant compactly supported function is again locally constant complactly supported. In the case of $SL(2)$, we show that certain combinations of orbital integrals belong to the Bernstein center and reveal a geometric reason for this phenomenon.
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Additional Information
  • Allen Moy
  • Affiliation: Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong
  • MR Author ID: 127665
  • Email: amoy@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): September 17, 2004
  • Received by editor(s) in revised form: January 31, 2005
  • Published electronically: April 14, 2005
  • Additional Notes: The first author was partially supported by the National Science Foundation grant DMS–0100413 while at the University of Michigan, and also partially supported by Research Grants Council grant HKUST6112/02P
    The second author was partially supported by Croatian Ministry of Science and Technology grant #37108
  • © Copyright 2005 American Mathematical Society
  • Journal: Represent. Theory 9 (2005), 327-353
  • MSC (2000): Primary 22E50, 22E35
  • DOI: https://doi.org/10.1090/S1088-4165-05-00274-8
  • MathSciNet review: 2133763