{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:DP4GQ7XTWC2HRZ3Z3YLCFTF2PK","short_pith_number":"pith:DP4GQ7XT","schema_version":"1.0","canonical_sha256":"1bf8687ef3b0b478e779de1622ccba7a9b1483baffd43f9dee60511e875475cd","source":{"kind":"arxiv","id":"1012.0132","version":2},"attestation_state":"computed","paper":{"title":"Extended weight semigroups of affine spherical homogeneous spaces of non-simple semisimple algebraic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Roman Avdeev","submitted_at":"2010-12-01T09:24:05Z","abstract_excerpt":"The extended weight semigroup of a homogeneous space G/H of a connected semisimple algebraic group G characterizes the spectra of the representations of G on the spaces of regular sections of homogeneous linear bundles over G/H, including the space of regular functions on G/H. We compute the extended weight semigroups for all strictly irreducible affine spherical homogeneous spaces G/H, where G is a simply connected non-simple semisimple complex algebraic group and H a connected closed subgroup of it. In all the cases we also find the highest weight functions corresponding to the indecomposabl"},"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":"1012.0132","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-12-01T09:24:05Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"ae83637c20f4ac4dd35f3132e08c409ac1e16d86fcf2ab7f98e0d17706276934","abstract_canon_sha256":"2e3373d3c89b4b5014527431547ba90ddb6effd087849a978f4999a58374271b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:24.450245Z","signature_b64":"/S3Pd5t1leEorxrFONoU6c/0LszyVMhKB/l8MIx65n8DYeXxHESvmMf3dKOwIMRcK/2TMmieJfOT00emf7UwCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1bf8687ef3b0b478e779de1622ccba7a9b1483baffd43f9dee60511e875475cd","last_reissued_at":"2026-05-18T04:08:24.449706Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:24.449706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extended weight semigroups of affine spherical homogeneous spaces of non-simple semisimple algebraic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Roman Avdeev","submitted_at":"2010-12-01T09:24:05Z","abstract_excerpt":"The extended weight semigroup of a homogeneous space G/H of a connected semisimple algebraic group G characterizes the spectra of the representations of G on the spaces of regular sections of homogeneous linear bundles over G/H, including the space of regular functions on G/H. We compute the extended weight semigroups for all strictly irreducible affine spherical homogeneous spaces G/H, where G is a simply connected non-simple semisimple complex algebraic group and H a connected closed subgroup of it. In all the cases we also find the highest weight functions corresponding to the indecomposabl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0132","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":""},"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":"1012.0132","created_at":"2026-05-18T04:08:24.449799+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.0132v2","created_at":"2026-05-18T04:08:24.449799+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.0132","created_at":"2026-05-18T04:08:24.449799+00:00"},{"alias_kind":"pith_short_12","alias_value":"DP4GQ7XTWC2H","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"DP4GQ7XTWC2HRZ3Z","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"DP4GQ7XT","created_at":"2026-05-18T12:26:06.534383+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/DP4GQ7XTWC2HRZ3Z3YLCFTF2PK","json":"https://pith.science/pith/DP4GQ7XTWC2HRZ3Z3YLCFTF2PK.json","graph_json":"https://pith.science/api/pith-number/DP4GQ7XTWC2HRZ3Z3YLCFTF2PK/graph.json","events_json":"https://pith.science/api/pith-number/DP4GQ7XTWC2HRZ3Z3YLCFTF2PK/events.json","paper":"https://pith.science/paper/DP4GQ7XT"},"agent_actions":{"view_html":"https://pith.science/pith/DP4GQ7XTWC2HRZ3Z3YLCFTF2PK","download_json":"https://pith.science/pith/DP4GQ7XTWC2HRZ3Z3YLCFTF2PK.json","view_paper":"https://pith.science/paper/DP4GQ7XT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.0132&json=true","fetch_graph":"https://pith.science/api/pith-number/DP4GQ7XTWC2HRZ3Z3YLCFTF2PK/graph.json","fetch_events":"https://pith.science/api/pith-number/DP4GQ7XTWC2HRZ3Z3YLCFTF2PK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DP4GQ7XTWC2HRZ3Z3YLCFTF2PK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DP4GQ7XTWC2HRZ3Z3YLCFTF2PK/action/storage_attestation","attest_author":"https://pith.science/pith/DP4GQ7XTWC2HRZ3Z3YLCFTF2PK/action/author_attestation","sign_citation":"https://pith.science/pith/DP4GQ7XTWC2HRZ3Z3YLCFTF2PK/action/citation_signature","submit_replication":"https://pith.science/pith/DP4GQ7XTWC2HRZ3Z3YLCFTF2PK/action/replication_record"}},"created_at":"2026-05-18T04:08:24.449799+00:00","updated_at":"2026-05-18T04:08:24.449799+00:00"}