{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:6ZM75DIYKYXVJGF7OUMBRTW5UI","short_pith_number":"pith:6ZM75DIY","schema_version":"1.0","canonical_sha256":"f659fe8d18562f5498bf751818cedda221c37b71af21eb48d8a325c39f67548b","source":{"kind":"arxiv","id":"1401.0055","version":1},"attestation_state":"computed","paper":{"title":"The adjoint representation of a Lie algebra and the support of Kostant's weight multiplicity formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Erik Insko, Lauren Kelly Williams, Pamela E. Harris","submitted_at":"2013-12-30T23:45:16Z","abstract_excerpt":"Even though weight multiplicity formulas, such as Kostant's formula, exist their computational use is extremely cumbersome. In fact, even in cases when the multiplicity is well understood, the number of terms considered in Kostant's formula is factorial in the rank of the Lie algebra and the value of the partition function is unknown. In this paper we address the difficult question: What are the contributing terms to the multiplicity of the zero weight in the adjoint representation of a finite dimensional Lie algebra? We describe and enumerate the cardinalities of these sets (through linear ho"},"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":"1401.0055","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-12-30T23:45:16Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"9a511bb5a7fd5f5db1ab257b8eadca8685784d0c56f425874ae99bbb8ced1c17","abstract_canon_sha256":"fa20cbf5f9042ccc062a4fcef9c879e6acc506c31a2cbcb850ec9c6cc07aea58"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:31.213599Z","signature_b64":"W4QJel9PE4M8L1jZ8RauQRzEvKh4smeGwtKXaZlWAzgboZ7/sxo8hqFHV6LjW5KQ8kBkIZblGP/X+K96sS6YDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f659fe8d18562f5498bf751818cedda221c37b71af21eb48d8a325c39f67548b","last_reissued_at":"2026-05-18T03:03:31.212807Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:31.212807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The adjoint representation of a Lie algebra and the support of Kostant's weight multiplicity formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Erik Insko, Lauren Kelly Williams, Pamela E. Harris","submitted_at":"2013-12-30T23:45:16Z","abstract_excerpt":"Even though weight multiplicity formulas, such as Kostant's formula, exist their computational use is extremely cumbersome. In fact, even in cases when the multiplicity is well understood, the number of terms considered in Kostant's formula is factorial in the rank of the Lie algebra and the value of the partition function is unknown. In this paper we address the difficult question: What are the contributing terms to the multiplicity of the zero weight in the adjoint representation of a finite dimensional Lie algebra? We describe and enumerate the cardinalities of these sets (through linear ho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0055","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":"1401.0055","created_at":"2026-05-18T03:03:31.212937+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.0055v1","created_at":"2026-05-18T03:03:31.212937+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0055","created_at":"2026-05-18T03:03:31.212937+00:00"},{"alias_kind":"pith_short_12","alias_value":"6ZM75DIYKYXV","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"6ZM75DIYKYXVJGF7","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"6ZM75DIY","created_at":"2026-05-18T12:27:36.564083+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/6ZM75DIYKYXVJGF7OUMBRTW5UI","json":"https://pith.science/pith/6ZM75DIYKYXVJGF7OUMBRTW5UI.json","graph_json":"https://pith.science/api/pith-number/6ZM75DIYKYXVJGF7OUMBRTW5UI/graph.json","events_json":"https://pith.science/api/pith-number/6ZM75DIYKYXVJGF7OUMBRTW5UI/events.json","paper":"https://pith.science/paper/6ZM75DIY"},"agent_actions":{"view_html":"https://pith.science/pith/6ZM75DIYKYXVJGF7OUMBRTW5UI","download_json":"https://pith.science/pith/6ZM75DIYKYXVJGF7OUMBRTW5UI.json","view_paper":"https://pith.science/paper/6ZM75DIY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.0055&json=true","fetch_graph":"https://pith.science/api/pith-number/6ZM75DIYKYXVJGF7OUMBRTW5UI/graph.json","fetch_events":"https://pith.science/api/pith-number/6ZM75DIYKYXVJGF7OUMBRTW5UI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6ZM75DIYKYXVJGF7OUMBRTW5UI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6ZM75DIYKYXVJGF7OUMBRTW5UI/action/storage_attestation","attest_author":"https://pith.science/pith/6ZM75DIYKYXVJGF7OUMBRTW5UI/action/author_attestation","sign_citation":"https://pith.science/pith/6ZM75DIYKYXVJGF7OUMBRTW5UI/action/citation_signature","submit_replication":"https://pith.science/pith/6ZM75DIYKYXVJGF7OUMBRTW5UI/action/replication_record"}},"created_at":"2026-05-18T03:03:31.212937+00:00","updated_at":"2026-05-18T03:03:31.212937+00:00"}