Depth-zero base change for ramified U(2,1)

TL;DR

This paper provides an explicit description of base change for depth-zero representations of ramified unitary groups, demonstrating compatibility with finite group representations and proposing broader conjectures.

Contribution

It introduces a detailed description of L-packets and quadratic base change for ramified U(2,1), and shows compatibility with finite group representation liftings.

Findings

Explicit description of L-packets for ramified U(2,1)

Demonstration of base change compatibility with finite group representations

Conjecture on broader applicability of this compatibility

Abstract

We give an explicit description of L-packets and quadratic base change for depth-zero representations of ramified unitary groups in two and three variables. We show that this base change lifting is compatible with a certain lifting of families of representations of finite groups. We conjecture that such a compatibility is valid in much greater generality.