{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:VXI2JUMZ35N6BY6WOINMSUEAEO","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":"ba01dda98e3ed6844d0ea78135b5b4bc0541b114e20faaec9c0ca646908b6642","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-03-27T12:33:40Z","title_canon_sha256":"78ae7cf004fa249e37076f6c9d39f74dadb36ae21ec8700f440e460e09414470"},"schema_version":"1.0","source":{"id":"1303.6806","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.6806","created_at":"2026-05-18T03:26:22Z"},{"alias_kind":"arxiv_version","alias_value":"1303.6806v2","created_at":"2026-05-18T03:26:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.6806","created_at":"2026-05-18T03:26:22Z"},{"alias_kind":"pith_short_12","alias_value":"VXI2JUMZ35N6","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VXI2JUMZ35N6BY6W","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VXI2JUMZ","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:31e120c53afa5853bb3aba39290fdec40b2da2375d57228b5724000e6dd8c90f","target":"graph","created_at":"2026-05-18T03:26:22Z","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":"We provide a direct connection between Springer theory, via Green polynomials, the irreducible representations of the pin cover $\\wti W$, a certain double cover of the Weyl group $W$, and an extended Dirac operator for graded Hecke algebras. Our approach leads to a new and uniform construction of the irreducible genuine $\\wti W$-characters. In the process, we give a construction of the action by an outer automorphism of the Dynkin diagram on the cohomology groups of Springer theory, and we also introduce a $q$-elliptic pairing for $W$ with respect to the reflection representation $V$. These co","authors_text":"Dan Ciubotaru, Xuhua He","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-03-27T12:33:40Z","title":"Green polynomials of Weyl groups, elliptic pairings, and the extended Dirac index"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6806","kind":"arxiv","version":2},"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":"sha256:0697fc6cab37b8eb53880f18e0333b6c1542a35617cdc9d93a37cc9d7b33e7cf","target":"record","created_at":"2026-05-18T03:26:22Z","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":"ba01dda98e3ed6844d0ea78135b5b4bc0541b114e20faaec9c0ca646908b6642","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-03-27T12:33:40Z","title_canon_sha256":"78ae7cf004fa249e37076f6c9d39f74dadb36ae21ec8700f440e460e09414470"},"schema_version":"1.0","source":{"id":"1303.6806","kind":"arxiv","version":2}},"canonical_sha256":"add1a4d199df5be0e3d6721ac95080238c3c70faf54c2cd4d6e3b154385f1499","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"add1a4d199df5be0e3d6721ac95080238c3c70faf54c2cd4d6e3b154385f1499","first_computed_at":"2026-05-18T03:26:22.338156Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:22.338156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2G1OcGRhTjCxmgqh3AovvaHa6vFKfKCE9UnZJgyPYfZBFhcwGpEryb9AABBw7pWc2u+jtIQE51h0H5T/5c3zDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:22.340418Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.6806","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0697fc6cab37b8eb53880f18e0333b6c1542a35617cdc9d93a37cc9d7b33e7cf","sha256:31e120c53afa5853bb3aba39290fdec40b2da2375d57228b5724000e6dd8c90f"],"state_sha256":"ae191ef84afdcada8048ad7b321ee72a0515fdfefb46238e17475bb07caa2726"}