{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:JF7H6FA4H3WZ5REOJ2JFYNHM3T","short_pith_number":"pith:JF7H6FA4","schema_version":"1.0","canonical_sha256":"497e7f141c3eed9ec48e4e925c34ecdce74914b0fb4f1a90e7ad090c5c4638b9","source":{"kind":"arxiv","id":"0903.1187","version":1},"attestation_state":"computed","paper":{"title":"Geometric Invariant Theory and Generalized Eigenvalue Problem II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Nicolas Ressayre (I3M)","submitted_at":"2009-03-06T10:59:18Z","abstract_excerpt":"Let $G$ be a connected reductive subgroup of a complex connected reductive group $\\hat{G}$. Fix maximal tori and Borel subgroups of $G$ and $\\hat{G}$. Consider the cone $LR^\\circ(\\hat{G},G)$ generated by the pairs $(\\nu,\\hat{\\nu})$ of strictly dominant characters such that $V_\\nu$ is a submodule of $V_{\\hat\\nu}$. The main result of this article is a bijective parametrisation of the faces of $LR^\\circ(\\hat G,G)$. We also explain when such a face is contained in another one. In way, we obtain results about the faces of the Dolgachev-Hu's $G$-ample cone. We also apply our results to reprove known"},"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":"0903.1187","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-03-06T10:59:18Z","cross_cats_sorted":[],"title_canon_sha256":"b0f3384483ed24367d7ecc58b84b4c07f59ffd8619b87f77aa198a3a55d70b9f","abstract_canon_sha256":"b090d9229e3244922b74bafaeb614e3510e62700b884543715ef4b4dd3186afe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:14:36.898886Z","signature_b64":"9/Z9hDNC91olGTqxfCLxKDLMN/rn4HO96zBCYFnHgotWo6ucOoMxYye6E4f8fxqWaLeA1Cj/Zk/wEGitBBORAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"497e7f141c3eed9ec48e4e925c34ecdce74914b0fb4f1a90e7ad090c5c4638b9","last_reissued_at":"2026-05-18T02:14:36.898255Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:14:36.898255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometric Invariant Theory and Generalized Eigenvalue Problem II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Nicolas Ressayre (I3M)","submitted_at":"2009-03-06T10:59:18Z","abstract_excerpt":"Let $G$ be a connected reductive subgroup of a complex connected reductive group $\\hat{G}$. Fix maximal tori and Borel subgroups of $G$ and $\\hat{G}$. Consider the cone $LR^\\circ(\\hat{G},G)$ generated by the pairs $(\\nu,\\hat{\\nu})$ of strictly dominant characters such that $V_\\nu$ is a submodule of $V_{\\hat\\nu}$. The main result of this article is a bijective parametrisation of the faces of $LR^\\circ(\\hat G,G)$. We also explain when such a face is contained in another one. In way, we obtain results about the faces of the Dolgachev-Hu's $G$-ample cone. We also apply our results to reprove known"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.1187","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0903.1187","created_at":"2026-05-18T02:14:36.898358+00:00"},{"alias_kind":"arxiv_version","alias_value":"0903.1187v1","created_at":"2026-05-18T02:14:36.898358+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.1187","created_at":"2026-05-18T02:14:36.898358+00:00"},{"alias_kind":"pith_short_12","alias_value":"JF7H6FA4H3WZ","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"JF7H6FA4H3WZ5REO","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"JF7H6FA4","created_at":"2026-05-18T12:26:00.592388+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/JF7H6FA4H3WZ5REOJ2JFYNHM3T","json":"https://pith.science/pith/JF7H6FA4H3WZ5REOJ2JFYNHM3T.json","graph_json":"https://pith.science/api/pith-number/JF7H6FA4H3WZ5REOJ2JFYNHM3T/graph.json","events_json":"https://pith.science/api/pith-number/JF7H6FA4H3WZ5REOJ2JFYNHM3T/events.json","paper":"https://pith.science/paper/JF7H6FA4"},"agent_actions":{"view_html":"https://pith.science/pith/JF7H6FA4H3WZ5REOJ2JFYNHM3T","download_json":"https://pith.science/pith/JF7H6FA4H3WZ5REOJ2JFYNHM3T.json","view_paper":"https://pith.science/paper/JF7H6FA4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0903.1187&json=true","fetch_graph":"https://pith.science/api/pith-number/JF7H6FA4H3WZ5REOJ2JFYNHM3T/graph.json","fetch_events":"https://pith.science/api/pith-number/JF7H6FA4H3WZ5REOJ2JFYNHM3T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JF7H6FA4H3WZ5REOJ2JFYNHM3T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JF7H6FA4H3WZ5REOJ2JFYNHM3T/action/storage_attestation","attest_author":"https://pith.science/pith/JF7H6FA4H3WZ5REOJ2JFYNHM3T/action/author_attestation","sign_citation":"https://pith.science/pith/JF7H6FA4H3WZ5REOJ2JFYNHM3T/action/citation_signature","submit_replication":"https://pith.science/pith/JF7H6FA4H3WZ5REOJ2JFYNHM3T/action/replication_record"}},"created_at":"2026-05-18T02:14:36.898358+00:00","updated_at":"2026-05-18T02:14:36.898358+00:00"}