{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:PZIHVQPNQ4XYV23GFHW4FOPQNQ","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":"716c0f51d19a0eefa5e5870b1df1cadc910938f3700e1cc7273110cc7825ad56","cross_cats_sorted":["math.AG","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-06-29T01:12:14Z","title_canon_sha256":"22c112d628675e2a7d58705602fe40f5c92320274a535556af558aa7f620ecf1"},"schema_version":"1.0","source":{"id":"0906.5189","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.5189","created_at":"2026-05-18T03:58:14Z"},{"alias_kind":"arxiv_version","alias_value":"0906.5189v4","created_at":"2026-05-18T03:58:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.5189","created_at":"2026-05-18T03:58:14Z"},{"alias_kind":"pith_short_12","alias_value":"PZIHVQPNQ4XY","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"PZIHVQPNQ4XYV23G","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"PZIHVQPN","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:86403a7c8ff54516364c3efefd157d654779976b7779a2e296b20e00b572c5f2","target":"graph","created_at":"2026-05-18T03:58:14Z","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":"Suppose a finite group acts on a scheme X and a finite-dimensional Lie algebra g. The corresponding equivariant map algebra is the Lie algebra M of equivariant regular maps from X to g. We classify the irreducible finite-dimensional representations of these algebras. In particular, we show that all such representations are tensor products of evaluation representations and one-dimensional representations, and we establish conditions ensuring that they are all evaluation representations. For example, this is always the case if M is perfect.\n  Our results can be applied to multiloop algebras, cur","authors_text":"Alistair Savage, Erhard Neher, Prasad Senesi","cross_cats":["math.AG","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-06-29T01:12:14Z","title":"Irreducible finite-dimensional representations of equivariant map algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.5189","kind":"arxiv","version":4},"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:d99b3ea8537c9653bcadab245e8561b248c7c290e086afa7001255cd3af2f6be","target":"record","created_at":"2026-05-18T03:58:14Z","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":"716c0f51d19a0eefa5e5870b1df1cadc910938f3700e1cc7273110cc7825ad56","cross_cats_sorted":["math.AG","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-06-29T01:12:14Z","title_canon_sha256":"22c112d628675e2a7d58705602fe40f5c92320274a535556af558aa7f620ecf1"},"schema_version":"1.0","source":{"id":"0906.5189","kind":"arxiv","version":4}},"canonical_sha256":"7e507ac1ed872f8aeb6629edc2b9f06c3499369909b0f31ee470804b3f215f4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e507ac1ed872f8aeb6629edc2b9f06c3499369909b0f31ee470804b3f215f4c","first_computed_at":"2026-05-18T03:58:14.338532Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:14.338532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cBFIg2pM+GOR+Kh0LJDy0hXwFGFxfQOm10a9kP/wXrS/63/sAyHGk6MtxyFVRFq675/77GGRfV2lUsNjXCzyDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:14.339018Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.5189","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d99b3ea8537c9653bcadab245e8561b248c7c290e086afa7001255cd3af2f6be","sha256:86403a7c8ff54516364c3efefd157d654779976b7779a2e296b20e00b572c5f2"],"state_sha256":"78cc66e254840bab6668e38796fe8fe844e8c03d8ef544ce5f2eb579dd79d809"}