Irreducible $p$-modular representations of unramified $U(2,1)$

Abstract

Let $E/F$ be a unramified quadratic extension of non-archimedean local fields of odd characteristic $p$, and $G$ be the unramified unitary group $U(2,1)(E/F)$. For an irreducible smooth representation $\pi$ of $G$ over ${\overline{\mathbf{F}}}_p$, with an underlying irreducible smooth representation $\sigma$ of a maximal compact open subgroup $K$, we prove that $\pi$ admits eigenvectors for an appropriate Hecke operator $T_{\sigma }$, and we classify those $\pi$ with non-zero eigenvalues for $T_{\sigma }$ by a tree argument; as a corollary, we show $\pi$ is supersingular if and only if it is supercuspidal.

The cooperation between the authors goes wrong, and the second author decided to terminate it. So this paper is withdrawn from arXiv

References in corpus (1)

• A Satake isomorphism in characteristic p