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

Moy, Allen; Tadić, Marko

doi:10.1090/S1088-4165-05-00274-8

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.

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