Conjugacy class asymptotics, orbital integrals, and the Bernstein center: the case of

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 | References | Similar Articles | Additional Information

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 , 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