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Let $\Delta_{k,a}$ and $\Delta_k $ be the $(k,a)$-generalized Laguerreoperator and the Dunkl Laplacian operator on $\mathbb{R}^n$, respectively. Theaim of this article is twofold. First, we prove a restriction theorem for theFourier-$\Delta_{k,a}$ transform. Next, as an application of the restrictionproblem, we establish Strichartz estimates for orthonormal families of initialdata for the Schr\"odinger propagator $e^{-i t \Delta_{k, a}} $ associated withthe operator $ \Delta_{k, a}$. Further, using the classical Strichartzestimates for the free Schr\"odinger propagator $e^{-i t \Delta_{k, a}} $ fororthonormal systems of initial data and the kernel relation between thesemigroups $e^{-i t \Delta_{k, a}}$ and $e^{i \frac{t}{a}\|x\|^{2-a}\Delta_{k}},$ we prove Strichartz estimates for orthonormal systems of initialdata associated with the Dunkl operator $ \Delta_k $ on $\mathbb{R}^n$.Finally, we present some applications to our aforementioned results.

Orthonormal Strichartz inequalities for the $(k, a)$-generalized Laguerre operator and Dunkl operator