{"paper":{"title":"Octonionic structure operator and its right spectrum","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG","math.RT"],"primary_cat":"math.RA","authors_text":"Sergey Grigorian","submitted_at":"2026-06-06T18:52:03Z","abstract_excerpt":"We study a canonical $G_2$-equivariant operator $h:\\mathbb{O}\\otimes_{\\mathbb{R}}V\\to \\mathbb{O}\\otimes_{\\mathbb{R}}V$ defined using only octonion multiplication, where $V$ is the standard $7$-dimensional $G_2$-module. We first compute its ordinary real spectrum using the $G_2$-decomposition of $\\mathbb{O}\\otimes_{\\mathbb{R}}V$. We then analyze the octonionic right-eigenvalue problem $$ h(\\widehat w)=\\widehat w\\lambda, \\qquad \\lambda\\in\\mathbb{O}. $$ After fixing a complex slice $\\mathbb{R}\\oplus\\mathbb{R}\\widehat u\\subset\\mathbb{O}$, the problem becomes a real spectral problem for $H_{u,Q}=h-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08299","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.08299/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}