{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:G4KJ5LC7ONACYT4KPVCOLDMGOH","short_pith_number":"pith:G4KJ5LC7","canonical_record":{"source":{"id":"1806.06181","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-06-16T04:50:44Z","cross_cats_sorted":[],"title_canon_sha256":"0d337395308503e284a98ab518f19157c1953afea54cf8f6be12c739ab9e42e1","abstract_canon_sha256":"2c33aa471a465f6f23a90a955b3e6d3412375f4abc4ecacecf1679391ff8d6d6"},"schema_version":"1.0"},"canonical_sha256":"37149eac5f73402c4f8a7d44e58d8671ed23adfa96424fd94385e45e0e4c8d84","source":{"kind":"arxiv","id":"1806.06181","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.06181","created_at":"2026-05-18T00:13:03Z"},{"alias_kind":"arxiv_version","alias_value":"1806.06181v1","created_at":"2026-05-18T00:13:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.06181","created_at":"2026-05-18T00:13:03Z"},{"alias_kind":"pith_short_12","alias_value":"G4KJ5LC7ONAC","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"G4KJ5LC7ONACYT4K","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"G4KJ5LC7","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:G4KJ5LC7ONACYT4KPVCOLDMGOH","target":"record","payload":{"canonical_record":{"source":{"id":"1806.06181","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-06-16T04:50:44Z","cross_cats_sorted":[],"title_canon_sha256":"0d337395308503e284a98ab518f19157c1953afea54cf8f6be12c739ab9e42e1","abstract_canon_sha256":"2c33aa471a465f6f23a90a955b3e6d3412375f4abc4ecacecf1679391ff8d6d6"},"schema_version":"1.0"},"canonical_sha256":"37149eac5f73402c4f8a7d44e58d8671ed23adfa96424fd94385e45e0e4c8d84","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:03.413376Z","signature_b64":"vkKUY2BMfesKnJTzWzrCqTPGpxOFhq1q4C3GRWTDEUcN5qO55s/ctoNvtbdRdq/gRsPEUNSYxhcdG4KCtu1xBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37149eac5f73402c4f8a7d44e58d8671ed23adfa96424fd94385e45e0e4c8d84","last_reissued_at":"2026-05-18T00:13:03.412747Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:03.412747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.06181","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:13:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OGKyZoRwFDFSh0inlb4sRMGUlJHvIMPRp/XtCIskJcdmjGMWpnFaOwig+2xxSba1l9yaFfFfX7dNR7oEuAzxAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:23:59.776859Z"},"content_sha256":"5feb9456bd0ad695909246e98322c417261bf653091d455e9d3cf2d87b4ec0a3","schema_version":"1.0","event_id":"sha256:5feb9456bd0ad695909246e98322c417261bf653091d455e9d3cf2d87b4ec0a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:G4KJ5LC7ONACYT4KPVCOLDMGOH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Peter--Weyl Iwahori algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Allen Moy, Dan Barbasch","submitted_at":"2018-06-16T04:50:44Z","abstract_excerpt":"The Peter-Weyl idempotent $e_{\\mathcal{P}}$ of a parahoric subgroup ${\\mathcal{P}}$ is the sum of the idempotents of irreducible representations of $\\mathcal{P}$ which have a nonzero Iwahori fixed vector. The convolution algebra associated to $e_{\\mathcal{P}}$ is called a Peter-Weyl Iwahori algebra. We show any Peter-Weyl Iwahori algebra is Morita equivalent to the Iwahori-Hecke algebra. Both the Iwahori-Hecke algebra and a Peter-Weyl Iwahori algbera have a natural $\\mathbb{C}^\\star$-algebra structure, and the Morita equivalence preserves irreducible hermitian and unitary modules. Both algebra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06181","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:13:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yDZX8HAp0Pj6Fle97HLddFHRzcsu754QKLde6O2iTeeYUsemm+r58kzD8R6vCLYMoArKf8TbgJcW35xJcUx+CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:23:59.777210Z"},"content_sha256":"1cdd3348f83b2f809c6b7da637efada5573ea8a885d3d16bfa6b38a083535809","schema_version":"1.0","event_id":"sha256:1cdd3348f83b2f809c6b7da637efada5573ea8a885d3d16bfa6b38a083535809"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G4KJ5LC7ONACYT4KPVCOLDMGOH/bundle.json","state_url":"https://pith.science/pith/G4KJ5LC7ONACYT4KPVCOLDMGOH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G4KJ5LC7ONACYT4KPVCOLDMGOH/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T13:23:59Z","links":{"resolver":"https://pith.science/pith/G4KJ5LC7ONACYT4KPVCOLDMGOH","bundle":"https://pith.science/pith/G4KJ5LC7ONACYT4KPVCOLDMGOH/bundle.json","state":"https://pith.science/pith/G4KJ5LC7ONACYT4KPVCOLDMGOH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G4KJ5LC7ONACYT4KPVCOLDMGOH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:G4KJ5LC7ONACYT4KPVCOLDMGOH","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":"2c33aa471a465f6f23a90a955b3e6d3412375f4abc4ecacecf1679391ff8d6d6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-06-16T04:50:44Z","title_canon_sha256":"0d337395308503e284a98ab518f19157c1953afea54cf8f6be12c739ab9e42e1"},"schema_version":"1.0","source":{"id":"1806.06181","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.06181","created_at":"2026-05-18T00:13:03Z"},{"alias_kind":"arxiv_version","alias_value":"1806.06181v1","created_at":"2026-05-18T00:13:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.06181","created_at":"2026-05-18T00:13:03Z"},{"alias_kind":"pith_short_12","alias_value":"G4KJ5LC7ONAC","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"G4KJ5LC7ONACYT4K","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"G4KJ5LC7","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:1cdd3348f83b2f809c6b7da637efada5573ea8a885d3d16bfa6b38a083535809","target":"graph","created_at":"2026-05-18T00:13:03Z","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":"The Peter-Weyl idempotent $e_{\\mathcal{P}}$ of a parahoric subgroup ${\\mathcal{P}}$ is the sum of the idempotents of irreducible representations of $\\mathcal{P}$ which have a nonzero Iwahori fixed vector. The convolution algebra associated to $e_{\\mathcal{P}}$ is called a Peter-Weyl Iwahori algebra. We show any Peter-Weyl Iwahori algebra is Morita equivalent to the Iwahori-Hecke algebra. Both the Iwahori-Hecke algebra and a Peter-Weyl Iwahori algbera have a natural $\\mathbb{C}^\\star$-algebra structure, and the Morita equivalence preserves irreducible hermitian and unitary modules. Both algebra","authors_text":"Allen Moy, Dan Barbasch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-06-16T04:50:44Z","title":"Peter--Weyl Iwahori algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06181","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":"sha256:5feb9456bd0ad695909246e98322c417261bf653091d455e9d3cf2d87b4ec0a3","target":"record","created_at":"2026-05-18T00:13:03Z","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":"2c33aa471a465f6f23a90a955b3e6d3412375f4abc4ecacecf1679391ff8d6d6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-06-16T04:50:44Z","title_canon_sha256":"0d337395308503e284a98ab518f19157c1953afea54cf8f6be12c739ab9e42e1"},"schema_version":"1.0","source":{"id":"1806.06181","kind":"arxiv","version":1}},"canonical_sha256":"37149eac5f73402c4f8a7d44e58d8671ed23adfa96424fd94385e45e0e4c8d84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37149eac5f73402c4f8a7d44e58d8671ed23adfa96424fd94385e45e0e4c8d84","first_computed_at":"2026-05-18T00:13:03.412747Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:03.412747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vkKUY2BMfesKnJTzWzrCqTPGpxOFhq1q4C3GRWTDEUcN5qO55s/ctoNvtbdRdq/gRsPEUNSYxhcdG4KCtu1xBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:03.413376Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.06181","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5feb9456bd0ad695909246e98322c417261bf653091d455e9d3cf2d87b4ec0a3","sha256:1cdd3348f83b2f809c6b7da637efada5573ea8a885d3d16bfa6b38a083535809"],"state_sha256":"817f18b39ec0391de14bdb5c1e35bb11c10ba85767381fad2da4e76d07c35cd1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DjREEfWo8Ek2MzuW3FIQJHlDLMlbVDY0PbrC9GVOFOTuVD2uLUstMDnae3+5Tc7pvMBX36wZPUnGl1g3icraBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T13:23:59.779212Z","bundle_sha256":"1780e28d6826c2b05d099557c0e418afae29690276053ecc005397a61443ac51"}}