On the upper bound of the multiplicities of Fourier-Jacobi models over finite fields

TL;DR

This paper establishes a uniform upper bound on the multiplicities of Fourier-Jacobi models over finite fields, confirming a conjecture and advancing understanding of their representation theory.

Contribution

It proves an upper bound on Fourier-Jacobi model multiplicities over finite fields, independent of the field size, and confirms a conjecture by Hiss and Schröer.

Findings

Established an upper bound for multiplicities independent of q

Proved a conjecture of Hiss and Schröer

Enhanced understanding of Fourier-Jacobi models over finite fields

Abstract

In general the multiplicity one theorem fails for Fourier-Jacobi models over finite fields. In this paper we prove that there is an upper bound for the multiplicities of Fourier-Jacobi models which is independent of $q$. As a consequence, we prove a conjecture of Hiss and Schr\"oer.