### Representation equivalence and $p$-spectra of constant curvature space forms

Roberto Miatello

 Let $\Gamma$ be a discrete subgroup acting without fixed points on a simply connected constant curvature space $X=G/K$, where $G$ is the full isometry group of $X$ and $K=O(n)$. We will relate the eigenspaces of the Hodge-Laplace operator on $p$-forms on $X$ with the irreducible constituents of the right regular representation of $G$ on $L^2(\Gamma\backslash G)$. As a consequence, we will relate the notions of p-isospectrality with $\tau_p$-representation equivalence, extending results of Pesce in this context.