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

## TL;DR

This paper investigates how irreducible smooth mod p representations of the unramified unitary group U(2,1) restrict to its Borel subgroup, extending known results from GL(2) to a more complex group.

## Contribution

It extends the understanding of restriction problems from GL(2) to the unramified unitary group U(2,1), providing new analogous results.

## Key findings

- Results on restriction of representations to Borel subgroup
- Analogies with Paškūnas' work on GL(2)
- New insights into mod p representations of U(2,1)

## 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}).