Abstract
We introduce, for a reductive p-adic group, a notion of split fundamental stratum of positive level playing the expected part in the type theory of Bushnell and Kutzko. In particular, we prove that a smooth representation containing such a stratum cannot be supercuspidal. The idea consists in deforming the stratum so that the Abelian character associated with the deformed stratum will be contained in the representation and will verify a “good” intertwining formula.
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