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On the constructions of supercuspidal representations

Abstract : In a first part, we compare Bushnell-Kutzko's and Yu's constructions of supercuspidal representations. In a tame situation, at each step of Bushnell-Kutzko's construction, we associated a part of a Yu datum. We finally get a link between these constructions when they are both defined: GLN in the tame case. In a second part we define analytic filtrations. For any rational point x in the reduced Bruhat-Tits building of G and any positive rational number r, we introduce a k-affinoid groupGₓ,ᵣ contained in the Berkovich analytification Gªⁿ of G. The Shilov boundary of Gₓ,ᵣ is a singleton. In this way we obtain a topological cone, whose basis is the reduced Bruhat-Tits building and vertex the neutral element, inside Gªⁿ parametrizing the k-affinoid groups Gₓ,ᵣ. We also define filtrations for the Lie algebra. We state and prove various properties of analytic filtrations and compare them with Moy-Prasad ones.
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Arnaud Mayeux. On the constructions of supercuspidal representations. Algebraic Geometry [math.AG]. Université Sorbonne Paris Cité, 2019. English. ⟨NNT : 2019USPCC016⟩. ⟨tel-02866443⟩

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