{"paper":{"title":"Representation equivalence and p-Spectrum of constant curvature space forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.RT"],"primary_cat":"math.SP","authors_text":"Emilio A. Lauret, Juan Pablo Rossetti, Roberto J. Miatello","submitted_at":"2012-09-21T20:39:56Z","abstract_excerpt":"We study the $p$-spectrum of a locally symmetric space of constant curvature $\\Gamma\\backslash X$, in connection with the right regular representation of the full isometry group $G$ of $X$ on $L^2(\\Gamma\\backslash G)_{\\tau_p}$, where $\\tau_p$ is the complexified $p$-exterior representation of $\\mathrm{O}(n)$ on $\\bigwedge^p(\\mathbb{R}^n)_\\mathbb{C}$. We give an expression of the multiplicity $d_\\lambda(p,\\Gamma)$ of the eigenvalues of the $p$-Hodge-Laplace operator in terms of multiplicities $n_\\Gamma(\\pi)$ of specific irreducible unitary representations of $G$.\n  As a consequence, we extend r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4916","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}