{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6DRR46F4R45EXB7FSMJVMPR5OY","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":"26e51264bc4e36012951e5592df132bb8406ea2663e55222dcbcbf306ab2c87d","cross_cats_sorted":["math.CV","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-10-28T13:11:51Z","title_canon_sha256":"69886980378b96596b8653f0d86cd3504283261f93cffe4d128eab5d65194ba8"},"schema_version":"1.0","source":{"id":"1110.6324","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6324","created_at":"2026-05-18T04:09:57Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6324v1","created_at":"2026-05-18T04:09:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6324","created_at":"2026-05-18T04:09:57Z"},{"alias_kind":"pith_short_12","alias_value":"6DRR46F4R45E","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6DRR46F4R45EXB7F","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6DRR46F4","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:058bb055ef6ac79fbd1142e340d582419382a7532be426b20ed5320f2a6033cd","target":"graph","created_at":"2026-05-18T04:09:57Z","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 complex simple Lie group, and let $U \\subseteq G$ be a maximal compact subgroup. Assume that $G$ admits a homogenous space $X=G/Q=U/K$ which is a compact Hermitian symmetric space. Let $\\mathscr{L} \\rightarrow X$ be the ample line bundle which generates the Picard group of $X$. In this paper we study the restrictions to $K$ of the family $(H^0(X, \\mathscr{L}^k))_{k \\in \\N}$ of irreducible $G$-representations. We describe explicitly the moment polytopes for the moment maps $X \\rightarrow \\fk^*$ associated to positive integer multiples of the Kostant-Kirillov symplectic form on $X$,","authors_text":"Benjamin Schwarz, Henrik Sepp\\\"anen","cross_cats":["math.CV","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-10-28T13:11:51Z","title":"Symplectic branching laws and Hermitian symmetric spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6324","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":"sha256:903efd0de38e9bdf359716b9a64334bb2d26112177e84c4e0c9c589673bef4b7","target":"record","created_at":"2026-05-18T04:09:57Z","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":"26e51264bc4e36012951e5592df132bb8406ea2663e55222dcbcbf306ab2c87d","cross_cats_sorted":["math.CV","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-10-28T13:11:51Z","title_canon_sha256":"69886980378b96596b8653f0d86cd3504283261f93cffe4d128eab5d65194ba8"},"schema_version":"1.0","source":{"id":"1110.6324","kind":"arxiv","version":1}},"canonical_sha256":"f0e31e78bc8f3a4b87e59313563e3d7614025b8ccceaacca2d0315bb266efdcf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0e31e78bc8f3a4b87e59313563e3d7614025b8ccceaacca2d0315bb266efdcf","first_computed_at":"2026-05-18T04:09:57.047265Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:57.047265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3CxOOUcg/xOLoThUbmbr8P2Vc3OCQIBiz15Jqzzn5fGRs1ENhYaSmtLkJSdgOb2yaUk4ZGMI5M4kNhLEiBqtDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:57.047987Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.6324","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:903efd0de38e9bdf359716b9a64334bb2d26112177e84c4e0c9c589673bef4b7","sha256:058bb055ef6ac79fbd1142e340d582419382a7532be426b20ed5320f2a6033cd"],"state_sha256":"ea45a4b7dda944a6c9fbdffb29338b2a04cf96fe36f623fcec006fc1bdc265c1"}