On the Schatten exponent in orthonormal Strichartz estimate for the Dunkl operators

In \cite{PRA} and \cite{SSM} the orthonormal Strichartz estimates for the Schrödinger equation associated with the Dunkl Laplacian and the Dunkl-Hermite operator are obtained. In this article, we prove a necessary condition on the Schatten exponent for the above orthonormal Strichartz estimates, which turns out to be optimal for the Schrödinger equations associated with Laplacian and Hermite operator as a special case.