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First, we show that $\\mathcal{A}(n)^{Sp(2n)}$ and $\\mathcal{A}(n)^{GL(n)}$ are $\\mathcal{W}$-algebras of type $\\mathcal{W}(2,4,\\dots, 2n)$ and $\\mathcal{W}(2,3,\\dots, 2n+1)$, respectively. Using these results, we find minimal strong finite generating sets for $\\mathcal{A}(mn)^{Sp(2n)}$ and $\\mathcal{A}(mn)^{GL(n)}$ for all $m,n\\geq 1$. We compute the characters of the irreducible representations of $\\mathcal{A}(mn)^{Sp(2n)\\times SO(m)}$ and $\\m"},"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":"1404.2686","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-04-10T04:20:08Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"cee6d0756444a0bb86c1f815091849975c8bf55232ba48683fcb82e2c8b03386","abstract_canon_sha256":"5bacece61c6aef48d0c6f854591fc7e073549f4203ebb4bff3b68b163893b090"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:25:19.734364Z","signature_b64":"KrDJZg076fvkNYhU1jW2f73RMu4x5KX03jArwykC/pv8DeAxl42CJlJZOhn6fYhnZGj84NWleSw7fmPrhedVBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6e9a55b6321abe5abcd2b39a99aff03c3567809784f42527e3026bc4b8dd2cc","last_reissued_at":"2026-07-05T01:25:19.734000Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:25:19.734000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Orbifolds of symplectic fermion algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Andrew R. Linshaw, Thomas Creutzig","submitted_at":"2014-04-10T04:20:08Z","abstract_excerpt":"We present a systematic study of the orbifolds of the rank $n$ symplectic fermion algebra $\\mathcal{A}(n)$, which has full automorphism group $Sp(2n)$. First, we show that $\\mathcal{A}(n)^{Sp(2n)}$ and $\\mathcal{A}(n)^{GL(n)}$ are $\\mathcal{W}$-algebras of type $\\mathcal{W}(2,4,\\dots, 2n)$ and $\\mathcal{W}(2,3,\\dots, 2n+1)$, respectively. Using these results, we find minimal strong finite generating sets for $\\mathcal{A}(mn)^{Sp(2n)}$ and $\\mathcal{A}(mn)^{GL(n)}$ for all $m,n\\geq 1$. We compute the characters of the irreducible representations of $\\mathcal{A}(mn)^{Sp(2n)\\times SO(m)}$ and $\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2686","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/1404.2686/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1404.2686","created_at":"2026-07-05T01:25:19.734058+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.2686v2","created_at":"2026-07-05T01:25:19.734058+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2686","created_at":"2026-07-05T01:25:19.734058+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y3U2KW3DEGV6","created_at":"2026-07-05T01:25:19.734058+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y3U2KW3DEGV6LK6N","created_at":"2026-07-05T01:25:19.734058+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y3U2KW3D","created_at":"2026-07-05T01:25:19.734058+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Y3U2KW3DEGV6LK6NFM42TGX7AP","json":"https://pith.science/pith/Y3U2KW3DEGV6LK6NFM42TGX7AP.json","graph_json":"https://pith.science/api/pith-number/Y3U2KW3DEGV6LK6NFM42TGX7AP/graph.json","events_json":"https://pith.science/api/pith-number/Y3U2KW3DEGV6LK6NFM42TGX7AP/events.json","paper":"https://pith.science/paper/Y3U2KW3D"},"agent_actions":{"view_html":"https://pith.science/pith/Y3U2KW3DEGV6LK6NFM42TGX7AP","download_json":"https://pith.science/pith/Y3U2KW3DEGV6LK6NFM42TGX7AP.json","view_paper":"https://pith.science/paper/Y3U2KW3D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.2686&json=true","fetch_graph":"https://pith.science/api/pith-number/Y3U2KW3DEGV6LK6NFM42TGX7AP/graph.json","fetch_events":"https://pith.science/api/pith-number/Y3U2KW3DEGV6LK6NFM42TGX7AP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y3U2KW3DEGV6LK6NFM42TGX7AP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y3U2KW3DEGV6LK6NFM42TGX7AP/action/storage_attestation","attest_author":"https://pith.science/pith/Y3U2KW3DEGV6LK6NFM42TGX7AP/action/author_attestation","sign_citation":"https://pith.science/pith/Y3U2KW3DEGV6LK6NFM42TGX7AP/action/citation_signature","submit_replication":"https://pith.science/pith/Y3U2KW3DEGV6LK6NFM42TGX7AP/action/replication_record"}},"created_at":"2026-07-05T01:25:19.734058+00:00","updated_at":"2026-07-05T01:25:19.734058+00:00"}