{"paper":{"title":"Measures and generalizations of dual Littlewood identities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.QA"],"primary_cat":"math.CO","authors_text":"Bin Jiang, Naihuan Jing, Qianyi Ye, Zhijun Li, Zhongren Cai","submitted_at":"2026-07-15T20:54:09Z","abstract_excerpt":"We introduce three families of vectors $|\\underline{\\lambda}^{so}\\rangle$, $|\\underline{\\lambda}^{sp}\\rangle$ and $|\\underline{\\lambda}^{o}\\rangle$ parametrized by partitions in the Fock space by using products of adjoint vertex operators. We show that the quotient space of the dual vacuum vector is spanned by the partition vectors indexed by a special family of partitions. The partition-indexed vectors also help us to derive the dual Littlewood identities of types B, C, and D in a new manner associated to the special family of partitions. As an application, we obtain a new free fermionic cons"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.14362","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/2607.14362/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"}