{"paper":{"title":"Factorization of classical characters twisted by roots of unity: II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Nishu Kumari","submitted_at":"2022-12-23T17:10:18Z","abstract_excerpt":"Fix natural numbers $n \\geq 1$, $t \\geq 2$ and a primitive $t^{\\text{th}}$ root of unity $\\omega$. In previous work with A. Ayyer (J. Alg., 2022), we studied the factorization of specialized irreducible characters of $\\text{GL}_{tn}$, $\\text{SO}_{2tn+1},$ $\\text{Sp}_{2tn}$ and $\\text{O}_{2tn}$ evaluated at elements to $\\omega^j x_i$ for $0 \\leq j \\leq t-1$ and $1 \\leq i \\leq n$. In this work, we extend the results to the groups $\\text{GL}_{tn+m}$ $(0 \\leq m \\leq t-1)$, $\\text{SO}_{2tn+3}$, $\\text{Sp}_{2tn+2}$ and $\\text{O}_{2tn+2}$ evaluated at similar specializations: (1) for the $\\text{GL}_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.12477","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/2212.12477/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"}