{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:U6DL5Y7T35WBLLUPGAN6UEGVSX","short_pith_number":"pith:U6DL5Y7T","schema_version":"1.0","canonical_sha256":"a786bee3f3df6c15ae8f301bea10d595c6b52fbeb29744a4f80dfef631440117","source":{"kind":"arxiv","id":"1504.06522","version":3},"attestation_state":"computed","paper":{"title":"The PBW filtration and convex polytopes in type $\\tt B$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Deniz Kus, Teodor Backhaus","submitted_at":"2015-04-24T14:24:21Z","abstract_excerpt":"We study the PBW filtration on irreducible finite--dimensional representations for the Lie algebra of type $\\tt B_n$. We prove in several cases, including all multiples of the adjoint representation and all irreducible finite--dimensional representations for $\\tt B_3$, that there exists a normal polytope such that the lattice points of this polytope parametrize a basis of the corresponding associated graded space. As a consequence we obtain several classes of favourable modules and graded combinatorial character formulas."},"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":"1504.06522","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-04-24T14:24:21Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"7c943b3ed1168c6c70231cad88bb688319e55351d3066d7547112d23eab07542","abstract_canon_sha256":"569edea497fa3ad6ecc0ec14f176e528afb540b776bc6e6a260d2608dca63dc7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:44.124824Z","signature_b64":"Q8EAyD2kNpQD2AG2e3CRqaZZ5IlxNM0tettjq0GNb7/IFwbYGecm5PaQlPaN8DLOVubNlmuSelfzY7B7t2cYCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a786bee3f3df6c15ae8f301bea10d595c6b52fbeb29744a4f80dfef631440117","last_reissued_at":"2026-05-18T00:07:44.124132Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:44.124132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The PBW filtration and convex polytopes in type $\\tt B$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Deniz Kus, Teodor Backhaus","submitted_at":"2015-04-24T14:24:21Z","abstract_excerpt":"We study the PBW filtration on irreducible finite--dimensional representations for the Lie algebra of type $\\tt B_n$. We prove in several cases, including all multiples of the adjoint representation and all irreducible finite--dimensional representations for $\\tt B_3$, that there exists a normal polytope such that the lattice points of this polytope parametrize a basis of the corresponding associated graded space. As a consequence we obtain several classes of favourable modules and graded combinatorial character formulas."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06522","kind":"arxiv","version":3},"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":"1504.06522","created_at":"2026-05-18T00:07:44.124247+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.06522v3","created_at":"2026-05-18T00:07:44.124247+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06522","created_at":"2026-05-18T00:07:44.124247+00:00"},{"alias_kind":"pith_short_12","alias_value":"U6DL5Y7T35WB","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"U6DL5Y7T35WBLLUP","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"U6DL5Y7T","created_at":"2026-05-18T12:29:44.643036+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/U6DL5Y7T35WBLLUPGAN6UEGVSX","json":"https://pith.science/pith/U6DL5Y7T35WBLLUPGAN6UEGVSX.json","graph_json":"https://pith.science/api/pith-number/U6DL5Y7T35WBLLUPGAN6UEGVSX/graph.json","events_json":"https://pith.science/api/pith-number/U6DL5Y7T35WBLLUPGAN6UEGVSX/events.json","paper":"https://pith.science/paper/U6DL5Y7T"},"agent_actions":{"view_html":"https://pith.science/pith/U6DL5Y7T35WBLLUPGAN6UEGVSX","download_json":"https://pith.science/pith/U6DL5Y7T35WBLLUPGAN6UEGVSX.json","view_paper":"https://pith.science/paper/U6DL5Y7T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.06522&json=true","fetch_graph":"https://pith.science/api/pith-number/U6DL5Y7T35WBLLUPGAN6UEGVSX/graph.json","fetch_events":"https://pith.science/api/pith-number/U6DL5Y7T35WBLLUPGAN6UEGVSX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U6DL5Y7T35WBLLUPGAN6UEGVSX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U6DL5Y7T35WBLLUPGAN6UEGVSX/action/storage_attestation","attest_author":"https://pith.science/pith/U6DL5Y7T35WBLLUPGAN6UEGVSX/action/author_attestation","sign_citation":"https://pith.science/pith/U6DL5Y7T35WBLLUPGAN6UEGVSX/action/citation_signature","submit_replication":"https://pith.science/pith/U6DL5Y7T35WBLLUPGAN6UEGVSX/action/replication_record"}},"created_at":"2026-05-18T00:07:44.124247+00:00","updated_at":"2026-05-18T00:07:44.124247+00:00"}