On some representations of the Iwahori subgroup

Stefano Morra (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

Abstract Let p 5 be a prime number. In 1994 Barthel and Livné gave a classification for irreducible representations of GL2 (F) over Fp , for F a p-adic field, discovering some objects, referred to as "supersingular", which appear as subquotients of a universal representations π(r, 0, 1). In this paper we give a detailed description the Iwahori structure of such universal representations for F an unramified extension of Qp . We determine a fractal structure which shows how and why the thechniques used for Qp fail and which let us determine"natural" subrepresentations of the universal object π(r, 0, 1). As a corollary, we get the Iwahori structure of tamely ramified principal series.

Mots clés: P-adic Langlands correspondence; Unramified extensions; Supersingular representations

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

Stefano Morra. On some representations of the Iwahori subgroup. Journal of Number Theory, 2012, 132 (5), pp.1047-1150. ⟨10.1016/j.jnt.2011.11.002⟩. ⟨hal-00576947v3⟩