Compatibility of theta lifts and tempered condition

TL;DR

This paper demonstrates that the metaplectic theta correspondence aligns with the tempered condition by direct matrix coefficient estimates, avoiding reliance on the classification theorem.

Contribution

It provides a new proof of compatibility between theta lifts and the tempered condition without using the classification theorem.

Findings

Established compatibility of theta lifts with tempered representations

Developed direct estimation method for matrix coefficients

Avoided reliance on classification theorem in proof

Abstract

In this note, we show that the metaplectic theta correspondence is compatible with the tempered condition by directly estimating the matrix coefficients, without using the classification theorem.