{"paper":{"title":"Higher orbitals of quizzy quantum group actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Teodor Banica","submitted_at":"2018-07-19T04:05:46Z","abstract_excerpt":"The hyperoctahedral group $H_N$ is known to have two natural liberations: the \"good\" one $H_N^+$, which is the quantum symmetry group of $N$ segments, and the \"bad\" one $\\bar{O}_N$, which is the quantum symmetry group of the $N$-hypercube. We study here this phenomenon, in the general \"quizzy\" framework, which covers the various liberations and twists of $H_N,O_N$. Our results include: (1) an interpretation of the embedding $\\bar{O}_N\\subset S_{2^N}^+$, as corresponding to the antisymmetric representation of $O_N$, (2) a study of the liberations of $H_N$, notably with the result $<H_N^+,\\bar{O"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07231","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}