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 $G{L}_2(F)$ (\cite{Pas07}).

Final version, accepted to appear in International Journal of Number Theory