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

Fang Shi

Published 2023-09-22Version 1

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.