The Jordan-Hölder series of the locally analytic Steinberg representation

Sascha Orlik , Benjamin Schraen (1)

1 LMV - Laboratoire de Mathématiques de Versailles

We determine the composition factors of a Jordan-Hölder series including multiplicities of the locally analytic Steinberg representation. For this purpose we prove the acyclicity of the evaluated locally analytic Tits complex giving rise to the Steinberg representation. Further we describe some analogue of the Jacquet functor applied to the irreducible principal series representation constructed by Orlik and Strauch.

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

Sascha Orlik, Benjamin Schraen. The Jordan-Hölder series of the locally analytic Steinberg representation. Documenta Mathematica, 2014, 19, pp.647-671. ⟨hal-00661701⟩