Correspondance de Langlands numerique pour la $\overline{\bf F}_p$-algebre de Hecke du pro-$p$-Iwahori de $GL_n(F)$.

Rachel Ollivier (1)

1 IMJ - Institut de Mathématiques de Jussieu

Let $F$ be a local non archimedean field of residue characteristic $p$. Let $H$ be the pro-$p$-Iwahori Hecke algebra of characteristic $p$ of $GL_n(F)$.An irreducible $H$-module with a null central character is called supersingular. We show that any irreducible supersingular $H$-module contains a character of the affine subring.As a result, the number of the irreducible supersingular $H$-modules of dimension $n$, with a fixed action of an uniformizer, is equal to the number of the irreducible mod $p$ representations of dimension $n$ of the local Weil group with a fixed value of the determinant on a Frobenius ([Vigneras]).

Domaines: Théorie des représentations [math.RT]

Rachel Ollivier. Correspondance de Langlands numerique pour la $\overline{\bf F}_p$-algebre de Hecke du pro-$p$-Iwahori de $GL_n(F)$.. 2003. ⟨hal-00000754v1⟩