$\ell$-modular representations of unramified $p$-adic U(2,1)

Abstract

We construct all irreducible cuspidal $\ell$-modular representations of a unitary group in three variables attached to an unramified extension of local fields of odd residual characteristic $p$ with $\ell \ne p$. We describe the $\ell$-modular principal series and show that the supercuspidal support of an irreducible $\ell$-modular representation is unique up to conjugacy.