Endomorphism algebras of admissible $p$-adic representations of $p$-adic Lie groups

Gabriel Dospinescu , Benjamin Schraen (1)

1 LMV - Laboratoire de Mathématiques de Versailles

Building on recent work of Ardakov and Wadsley, we prove Schur's lemma for absolutely irreducible admissible $p$-adic Banach space (respectively locally analytic) representations of $p$-adic Lie groups. We also prove finiteness results for the endomorphism algebra of an irreducible admissible representation.

Domaines: Théorie des représentations [math.RT]; Théorie des nombres [math.NT]

Gabriel Dospinescu, Benjamin Schraen. Endomorphism algebras of admissible $p$-adic representations of $p$-adic Lie groups. Representation theory, 2013, 17 (8), pp.237-246. ⟨10.1090/S1088-4165-2013-00432-6⟩. ⟨hal-00661700⟩