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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2304.13990","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2023-04-27T07:26:21Z","cross_cats_sorted":[],"title_canon_sha256":"7f89e3ba227b7dc502e7028cb91b0c00c5105711978fed4dc7f24f843d09795f","abstract_canon_sha256":"91ac4d597c8a1ce1dde1ccec527bfa1a203c49e821245805cda01b48adebe89b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:19:19.683453Z","signature_b64":"ccKZD2/YsUuIsWplXMcSHBu28JI72XXjGOY2v5uIWhIDUqwxAippauHelUSf6X7IjFkFshtm4RQLjWPVQkCaCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0879c015103a7dcbe720017618623bbc5c1dc879095e6fd0c8be9b12b14045e5","last_reissued_at":"2026-07-05T07:19:19.682924Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:19:19.682924Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $V^{\\lambda}_{ij}$. 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