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

Abstract: 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 $G$. In this note, we study the problem of the restriction of irreducible smooth $\overline{\mathbf{F}}_p$-representations of $G$ to $B$, and we obtain various results which are analogous to that of Pa$\check{\text{s}}$k$\bar{\text{u}}$nas on $GL_2 (F)$ (\cite{Pas07}).