{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QYB6B2BNM2SGPSFOPXAXBOCHPF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"fd336f82311acc794bea7269c69d879513f5bbe353ba8a926dfc78a96ff30bba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-10-06T17:07:11Z","title_canon_sha256":"a72f49c07f130186aff648767a5ca4a99c663334cb69df8198cd0f9b620c72ee"},"schema_version":"1.0","source":{"id":"1810.05084","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.05084","created_at":"2026-05-18T00:03:34Z"},{"alias_kind":"arxiv_version","alias_value":"1810.05084v1","created_at":"2026-05-18T00:03:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.05084","created_at":"2026-05-18T00:03:34Z"},{"alias_kind":"pith_short_12","alias_value":"QYB6B2BNM2SG","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"QYB6B2BNM2SGPSFO","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"QYB6B2BN","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:3d10c26e29794126a4887b556d3f6ce6f67fd2ae7e33566bb6e7d02b2c92ae2e","target":"graph","created_at":"2026-05-18T00:03:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $G$ be a finite group, $H$ be a normal subgroup of prime index $p$. Let $F$ be a field of either characteristic $0$ or prime to $|G|$. Let $\\eta$ be an irreducible $F$-representation of $H$. If $F$ is an algebraically closed field of characteristic either $0$ or prime to $|G|$, then the induced representation $\\eta \\uparrow^{G}_{H}$ is either irreducible or a direct sum of $p$ pairwise inequivalent irreducible representations. In this paper, we show that if $F$ is not assumed algebraically closed field, then there are five possibilities in the decomposition of induced representation into i","authors_text":"Soham Swadhin Pradhan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-10-06T17:07:11Z","title":"Representations induced from a normal subgroup of prime index"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05084","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1756755578fce19c0b9472539c61900cd05ef1b66dadddca33eb9211799dbbd0","target":"record","created_at":"2026-05-18T00:03:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"fd336f82311acc794bea7269c69d879513f5bbe353ba8a926dfc78a96ff30bba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-10-06T17:07:11Z","title_canon_sha256":"a72f49c07f130186aff648767a5ca4a99c663334cb69df8198cd0f9b620c72ee"},"schema_version":"1.0","source":{"id":"1810.05084","kind":"arxiv","version":1}},"canonical_sha256":"8603e0e82d66a467c8ae7dc170b84779472cf10c88e4b9ca2b0953f7921eb5c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8603e0e82d66a467c8ae7dc170b84779472cf10c88e4b9ca2b0953f7921eb5c6","first_computed_at":"2026-05-18T00:03:34.962061Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:34.962061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NEBhz6D7SyXx31QYzfd0oUq0Iz1D6JjCDXpDib8fJq8O0ejjSKxFCMMvOjGtn7lUurkQPUuVFtUcIblf7jILAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:34.962567Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.05084","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1756755578fce19c0b9472539c61900cd05ef1b66dadddca33eb9211799dbbd0","sha256:3d10c26e29794126a4887b556d3f6ce6f67fd2ae7e33566bb6e7d02b2c92ae2e"],"state_sha256":"b075231035bc4f6835d48102eda1921ac6f212ff3c00c2bb7c6778ec78b99ac0"}