{"paper":{"title":"Stability of the exterior cube $\\gamma$-factors for $\\mathrm{GL}(6)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Dongming She, Taiwang Deng","submitted_at":"2026-06-26T13:52:04Z","abstract_excerpt":"We prove the stability of the Langlands-Shahidi local $\\gamma$-factor for the exterior cube representation of $\\mathrm{GL}_6$. More precisely, if $\\pi_1$ and $\\pi_2$ are irreducible admissible generic representations of $\\mathrm{GL}_6(F)$ with the same central character, then \\[ \\gamma(s,\\pi_1\\otimes\\chi,\\wedge^3,\\psi)= \\gamma(s,\\pi_2\\otimes\\chi,\\wedge^3,\\psi) \\] for every sufficiently ramified character $\\chi$ of $F^\\times$, where $\\chi$ is regarded as a character of $\\mathrm{GL}_6(F)$ through the determinant. The proof uses the realization of the exterior cube representation by the maximal p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28091","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/2606.28091/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"}