Uniqueness of certain Fourier-Jacobi models over finite fields

TL;DR

This paper establishes the uniqueness of specific Fourier-Jacobi models for certain algebraic groups over finite fields, extending known results to new groups and settings.

Contribution

It proves the uniqueness of Fourier-Jacobi models for $G_2$, $Sp_4$, and $U_4$ over finite fields with odd characteristic, advancing the understanding of these models.

Findings

Uniqueness results for Fourier-Jacobi models of $G_2$, $Sp_4$, and $U_4$.

Extension of Fourier-Jacobi model uniqueness to finite fields.

Results applicable to groups over finite fields with odd characteristic.

Abstract

In this paper, we prove the uniqueness of certain Fourier-Jacobi models for the split exceptional group $G_2$ over finite fields with odd characteristic. Similar results are also proved for $Sp_4$ and $U_4$.