{"paper":{"title":"Gaussian Universality of Products Over Split Reductive Groups and the Satake Isomorphism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT","math.RT"],"primary_cat":"math.PR","authors_text":"Jiahe Shen","submitted_at":"2025-02-10T04:19:37Z","abstract_excerpt":"We establish that the singular numbers (arising from Cartan decomposition) and corners (emerging from Iwasawa decomposition) in split reductive groups over non-archimedean fields are fundamentally determined by Hall-Littlewood polynomials. Through applications of the Satake isomorphism, we extend Van Peski's results (arXiv:2011.09356, Theorem 1.3) to encompass arbitrary root systems. Leveraging this theoretical foundation, we further develop Shen's work (arXiv:2411.01104, Theorem 1.1) to demonstrate that both singular numbers and corners of such products exhibit minimal separation. This charac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.06143","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/2502.06143/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"}