{"paper":{"title":"Leading Terms of Relations on a Level 5 Module over the Twisted Affine Lie Algebra $A_2^{(2)}$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Arne Meurman, Mirko Primc, Stefano Capparelli","submitted_at":"2025-11-15T16:37:40Z","abstract_excerpt":"One of the starting points of this work was the duality of Borcea relating standard level $k$ representations of $A_1^{(1)}$ and level $2k+1$ of $A_2^{(2)}$. For $k=1$, the combinatorial bases in both cases yield the two Capparelli identities and we wanted to see if there is a correspondence between the bases in terms of partitions for all $k\\in\\mathbb N$. By using the vertex operator relations in the principal picture for level $5$ standard $A_2^{(2)}$-modules, we reduce a spanning set of Poincar\\'e-Birkhoff-Witt-type vectors in $L(5\\Lambda_0)$ by removing the leading terms of relations and r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.12284","kind":"arxiv","version":5},"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/2511.12284/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"}