Cuspidal types on $\textrm{GL}_{p}(\mathcal{O}_{F})$
Let $F$ be a non-Archimedean local field and let $\mathcal{O}_{F}$ be its ring of integers. We give a description of orbits of cuspidal types on $\mathrm{GL}_{p}( \mathcal{O}_{F})$, with $p$ prime. We determine which of them are regular representations and we provide an example which shows that an orbit of a representation does not always determine whether it is a cuspidal type or not.