Invariant elements under some congruence subgroups for irreducible GL2(Qp) representations over Fp

Stefano Morra (1)

1 LMV - Laboratoire de Mathématiques de Versailles

Let p be an odd prime number. Using the explicit description for irreducible GL2 (Qp )-representations over Fp made in our previous works, we determine all invariant elements of such representations under the actions of the congruence subgroups K_t , I_t , for any integer t>0. In particular, we have the dimension of the K_t -invariants for supersingular representations of GL2 (Qp ), for any t>1.

Mots clés: P-adic Langlands correspondence; Supersingular representation.; Supersingular representation

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

Stefano Morra. Invariant elements under some congruence subgroups for irreducible GL2(Qp) representations over Fp. Journal of Algebra, 2011, 339 (1), pp.252-303. ⟨10.1016/j.jalgebra.2011.02.043⟩. ⟨hal-00576945v1⟩