Vol. 254, No. 2, 2011

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Fourier transforms of semisimple orbital integrals on the Lie algebra of SL2

Loren Spice

Vol. 254 (2011), No. 2, 407–448
Abstract

The Harish-Chandra–Howe local character expansion expresses the characters of reductive, p  -adic groups in terms of Fourier transforms of nilpotent orbital integrals on their Lie algebras, and Murnaghan–Kirillov theory expresses many characters of reductive, p  -adic groups in terms of Fourier transforms of semisimple orbital integrals (also on their Lie algebras). In many cases, the evaluation of these Fourier transforms seems intractable, but for SL2  , the nilpotent orbital integrals have already been computed. We compute Fourier transforms of semisimple orbital integrals using a variant of Huntsinger’s integral formula and the theory of p  -adic special functions.

Keywords
p-adic, orbital integral, special function
Mathematical Subject Classification 2010
Primary: 22E35, 22E50
Milestones
Received: 7 October 2010
Accepted: 11 April 2011
Published: 27 February 2012
Authors
Loren Spice
Department of Mathematics
Texas Christian University
TCU Box 298900
2840 W. Bowie St
Fort Worth, TX 76109
United States
http://faculty.tcu.edu/lspice