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Let $\\phi$ be a non-trivial irreducible representation of $G$.\n  Then the Jordan normal form of $\\phi(u)$ contains at most one non-trivial block if and only if $G$ is of type $G_2$, $u$ is a regular unipotent element and $\\dim \\phi\\leq 7$.\n  Note that the irreducible representations of the simple classical algebraic groups in which a non-trivial "},"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":"1701.00125","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-12-31T15:55:24Z","cross_cats_sorted":[],"title_canon_sha256":"d70bdd25f1dc7bf374ea3f303441c15f87eeaa062da218b18efd3ab9095fd7a6","abstract_canon_sha256":"015cb6dafbef8e2278453c13ea32714ad92121f4bf5504842d017111bfbe64d3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:36.311640Z","signature_b64":"RYxi0Y/zjqaurKO77y/RYUKHupDSwkee2fp+mrG8cyCoRY9PpDxnmzUj6WFfpCwENGachGt+zqFbYJxCxM5mCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dba6a0c0b92dc5614b7672b3cad0451da630b287ffbc0592fa25c7cbee083c3d","last_reissued_at":"2026-05-18T00:53:36.311177Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:36.311177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Irreducible representations of simple algebraic groups in which a unipotent element is represented by a matrix with single non-trivial Jordan block","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alexandre Zalesski, Donna Testerman","submitted_at":"2016-12-31T15:55:24Z","abstract_excerpt":"In this paper we prove the following result.\n  Let $G$ be a simply connected simple linear algebraic group of exceptional Lie type over an algebraically closed field $F$ of characteristic $p\\geq 0$, and let $u\\in G$ be a nonidentity unipotent element. Let $\\phi$ be a non-trivial irreducible representation of $G$.\n  Then the Jordan normal form of $\\phi(u)$ contains at most one non-trivial block if and only if $G$ is of type $G_2$, $u$ is a regular unipotent element and $\\dim \\phi\\leq 7$.\n  Note that the irreducible representations of the simple classical algebraic groups in which a non-trivial "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00125","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1701.00125","created_at":"2026-05-18T00:53:36.311239+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.00125v1","created_at":"2026-05-18T00:53:36.311239+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00125","created_at":"2026-05-18T00:53:36.311239+00:00"},{"alias_kind":"pith_short_12","alias_value":"3OTKBQFZFXCW","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_16","alias_value":"3OTKBQFZFXCWCS3W","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_8","alias_value":"3OTKBQFZ","created_at":"2026-05-18T12:29:55.572404+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/3OTKBQFZFXCWCS3WOKZ4VUCFDW","json":"https://pith.science/pith/3OTKBQFZFXCWCS3WOKZ4VUCFDW.json","graph_json":"https://pith.science/api/pith-number/3OTKBQFZFXCWCS3WOKZ4VUCFDW/graph.json","events_json":"https://pith.science/api/pith-number/3OTKBQFZFXCWCS3WOKZ4VUCFDW/events.json","paper":"https://pith.science/paper/3OTKBQFZ"},"agent_actions":{"view_html":"https://pith.science/pith/3OTKBQFZFXCWCS3WOKZ4VUCFDW","download_json":"https://pith.science/pith/3OTKBQFZFXCWCS3WOKZ4VUCFDW.json","view_paper":"https://pith.science/paper/3OTKBQFZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.00125&json=true","fetch_graph":"https://pith.science/api/pith-number/3OTKBQFZFXCWCS3WOKZ4VUCFDW/graph.json","fetch_events":"https://pith.science/api/pith-number/3OTKBQFZFXCWCS3WOKZ4VUCFDW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3OTKBQFZFXCWCS3WOKZ4VUCFDW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3OTKBQFZFXCWCS3WOKZ4VUCFDW/action/storage_attestation","attest_author":"https://pith.science/pith/3OTKBQFZFXCWCS3WOKZ4VUCFDW/action/author_attestation","sign_citation":"https://pith.science/pith/3OTKBQFZFXCWCS3WOKZ4VUCFDW/action/citation_signature","submit_replication":"https://pith.science/pith/3OTKBQFZFXCWCS3WOKZ4VUCFDW/action/replication_record"}},"created_at":"2026-05-18T00:53:36.311239+00:00","updated_at":"2026-05-18T00:53:36.311239+00:00"}