l-modular representations of unramified p-adic U(2,1)

TL;DR

This paper constructs all cuspidal l-modular representations of a p-adic unitary group U(2,1) over an unramified extension, detailing principal series and supercuspidal support uniqueness.

Contribution

It provides a complete classification of cuspidal l-modular representations for U(2,1) in the unramified p-adic setting, including principal series and supercuspidal support analysis.

Findings

Constructed all cuspidal l-modular representations of U(2,1)

Described the l-modular principal series

Proved the supercuspidal support is unique up to conjugacy

Abstract

We construct all cuspidal l-modular representations of a unitary group in three variables attached to an unramified extension of local fields of odd residual characteristic p with l\neq p. We describe the l-modular principal series and show that the supercuspidal support of an irreducible l-modular representation is unique up to conjugacy.