Abstract
In this paper the authors develop a method to compute the local character expansion of a depth zero representation of a p-adic group. The main idea is to use the generalized Gelfand-Graev characters for finite groups as test functions to plug into the character formula. This is possible due to results of Waldspurger on the validity of the local character expansion in a large enough neighborhood of the identity. The method leads to a classification of the unipotent orbits in terms of parahoric subalgebras.
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