Restriction of $p$-modular representations of $U(2, 1)$ to a Borel subgroup

Peng Xu

Published 2019-02-06Version 1

Let $G$ be the unramified unitary group $U(2, 1)(E/F)$ defined over a non-archimedean local field $F$ of odd residue characteristic $p$, and $B$ be the standard Borel subgroup of $G$. We prove in this note that the restriction of any supersingular representation of $G$ to $B$ is irreducible, analogous to a result of Pa$\check{\text{s}}$k$\bar{\text{u}}$nas on $GL_2 (F)$.