Base change and theta correspondences for supercuspidal representations of SL(2)

TL;DR

This paper demonstrates the compatibility of quadratic base change and theta-lifting for supercuspidal representations of SL(2) over p-adic fields, using types and Weil representation models.

Contribution

It establishes a new compatibility result between base change and theta-lifting specifically for supercuspidal representations of SL(2,F).

Findings

Quadratic base change and theta-lifting are compatible for supercuspidal representations.

Uses the theory of types and lattice models of Weil representation.

Provides a framework for understanding representation transfers in p-adic groups.

Abstract

Let F be a p-adic field with p odd. Quadratic base change and theta-lifting are shown to be compatible for supercuspidal representations of SL(2,F). The argument involves the theory of types and the lattice model of the Weil representation.