Hecke modules and supersingular representations of U(2,1)

Abstract

Let F be a nonarchimedean local field of odd residual characteristic p. We classify finite-dimensional simple right modules for the pro-p-Iwahori-Hecke algebra ${\mathcal{H}}_C(G,I(1))$, where G is the unramified unitary group U(2,1)(E/F) in three variables. Using this description when C is the algebraic closure of ${\mathbb{F}}_p$, we define supersingular Hecke modules and show that the functor of I(1)-invariants induces a bijection between irreducible nonsupersingular mod-p representations of G and nonsupersingular simple right ${\mathcal{H}}_C(G,I(1))$-modules. We then use an argument of Paskunas to construct supersingular representations of G.

36 pages. Article shortened, results unchanged

References in corpus (2)

• The image of Colmez's Montreal functor
• Modulo $p$ parabolic induction of pro-$p$-Iwahori Hecke algebra

Cited by in corpus (1)

• A classification of the irreducible mod-p representations of U(1,1)(Q_p^2/Q_p)