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

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- by Allen Moy and Marko Tadić
- Represent. Theory
**9**(2005), 327-353 - DOI: https://doi.org/10.1090/S1088-4165-05-00274-8
- Published electronically: April 14, 2005
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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.## References

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## Bibliographic 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