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Conjugacy class asymptotics, orbital integrals, and the Bernstein center: the case of $SL(2)$


Authors: Allen Moy and Marko Tadic
Journal: Represent. Theory 9 (2005), 327-353
MSC (2000): Primary 22E50, 22E35
DOI: https://doi.org/10.1090/S1088-4165-05-00274-8
Published electronically: April 14, 2005
MathSciNet review: 2133763
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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
Email: amoy@ust.hk

Marko Tadic
Affiliation: Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia
Email: tadic@math.hr

DOI: https://doi.org/10.1090/S1088-4165-05-00274-8
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
Article copyright: © Copyright 2005 American Mathematical Society