Supercuspidal characters of reductive p-adic groups

Details Supercuspidal characters of reductive p-adic groups Supercuspidal characters of reductive p-adic groups

2007-07-23

arxiv.org/abs/0707.3313v4

Amer. J. Math., 131 (2009), no. 4, 1137-1210

Mathematics

Representation Theory

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

Scientific paper

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.

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