{"paper":{"title":"Cartesian symmetry classes associated with certain subgroups of S_m","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Seyyed Sadegh Gholami, Yousef Zamani","submitted_at":"2023-04-27T07:26:21Z","abstract_excerpt":"Let $V$ be an $n$-dimensional inner product space. Assume $G$ is a subgroup of the symmetric group of degree $m$, and $\\lambda$ is an irreducible character of $G$. Consider the \\emph{Cartesian symmetrizer} $C_{\\lambda}$ on the Cartesian space $\\times^{m}V$ defined by \\[ C_{\\lambda} = \\frac{\\lambda(1)}{|G|}\\sum_{\\tau\\in G} \\lambda(\\tau) Q(\\tau). \\] The vector space $ V^{\\lambda}(G) = C_{\\lambda}(\\times^{m}V) $ is called the Cartesian symmetry class associated with $G$ and $\\lambda$.\n  In this paper, we give a formula for the dimension of the cyclic subspace $V^{\\lambda}_{ij}$. Then we discuss t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.13990","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2304.13990/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"}