{"paper":{"title":"A decomposition of Weyl group multiple Dirichlet series for symmetrizable Kac-Moody root systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexandru A. Popa, Jack Walsh","submitted_at":"2026-07-13T17:26:45Z","abstract_excerpt":"We study twisted Weyl group multiple Dirichlet series attached to symmetrizable Kac-Moody root systems, using the Chinta-Gunnells method to construct their $p$-parts. Our main result is a decomposition theorem for functions invariant under the twisted Chinta-Gunnells action: under natural analytic hypotheses, such a function has a unique expansion in terms of shifted Chinta-Gunnells averages, indexed by the dominant weights in the highest weight module determined by the twisting parameter. In particular, we show that this decomposition holds for twisted multiple Dirichlet series over rational "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.11834","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/2607.11834/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"}