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This paper exploits the formalism of Moy and Prasad to sharpenand extend a result of Murnaghan. Let F be a nonarchimedean localeld ofresidual characteristic p &gt; n. We show that the character of a supercuspidalrepresentation of GLn (F ) can be expressed on a large set as its formal degreetimes the Fourier transform of an elliptic orbital integral. We prove a similarresult for tame, very supercuspidal representations of more general reductivegroups. Finally, we examine a consequence ...

Murnaghan-Kirillov theory for supercuspidal representations of tame general linear groups