Jeffrey D. Adler, Loren Spice
Published 2007-07-23, updated 2009-11-10Version 4
We compute the characters of many supercuspidal representations of reductive p-adic groups. Specifically, we deal with representations that arise via Yu's construction from data satisfying a certain compactness condition. Each character is expressed in terms of a depth-zero character of a smaller group, the (linear) characters appearing in Yu's construction, Fourier transforms of orbital integrals, and certain signs and cardinalities that are described explicitly in terms of the datum associated to the representation and of the element at which the character is evaluated.
Comments: 77 pages. In v.2: numbering changed; minor rewording; inserted Examples 1.4.2 and 1.5, and Lemma B.2. In v.3: minor re-wording; fixed a few sign errors in Proposition 3.8 and surrounding exposition. In v.4: fixed some minor errors
Journal: Amer. J. Math., 131 (2009), no. 4, 1137-1210
Supercuspidal characters of $\operatorname{SL}_2$ over a $p$-adic field
Genericity of supercuspidal representations of p-adic Sp(4)
Characters and growth of admissible representations of reductive p-adic groups
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