{"paper":{"title":"Orbits of subgroups of codimension one to four of the Iwahori group in the affine flag variety of $\\text{SL}_2$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Finite-dimensional Schubert cells in the affine flag variety of SL₂ decompose into orbits under a chain of Iwahori subgroups of codimensions one to four.","cross_cats":[],"primary_cat":"math.AG","authors_text":"Claude Eicher","submitted_at":"2026-05-13T07:01:53Z","abstract_excerpt":"We describe how each finite dimensional Schubert cell in the affine flag variety of $\\text{SL}_2$ decomposes into orbits for a chain of subgroups of codimension one to four of the Iwahori group."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We describe how each finite dimensional Schubert cell in the affine flag variety of SL₂ decomposes into orbits for a chain of subgroups of codimension one to four of the Iwahori group.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The subgroups of the Iwahori group form a well-defined chain of codimensions one to four for which an explicit orbit decomposition exists on every finite-dimensional Schubert cell.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Each finite-dimensional Schubert cell in the affine flag variety of SL₂ decomposes into orbits under a chain of Iwahori subgroups of codimension one to four.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Finite-dimensional Schubert cells in the affine flag variety of SL₂ decompose into orbits under a chain of Iwahori subgroups of codimensions one to four.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"f7621ad141f374b708bcdc9477539c019f1ec531d28d3b366fefc1acf2d87e00"},"source":{"id":"2605.13091","kind":"arxiv","version":1},"verdict":{"id":"c146002a-c7c5-4ca9-b2bd-e866848a7cff","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T18:37:20.281751Z","strongest_claim":"We describe how each finite dimensional Schubert cell in the affine flag variety of SL₂ decomposes into orbits for a chain of subgroups of codimension one to four of the Iwahori group.","one_line_summary":"Each finite-dimensional Schubert cell in the affine flag variety of SL₂ decomposes into orbits under a chain of Iwahori subgroups of codimension one to four.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The subgroups of the Iwahori group form a well-defined chain of codimensions one to four for which an explicit orbit decomposition exists on every finite-dimensional Schubert cell.","pith_extraction_headline":"Finite-dimensional Schubert cells in the affine flag variety of SL₂ decompose into orbits under a chain of Iwahori subgroups of codimensions one to four."},"references":{"count":3,"sample":[{"doi":"","year":null,"title":"A. Beilinson and V. Drinfeld. Quantization of Hitchin 's integrable system and Hecke eigensheaves . Unpublished","work_id":"a5c2f8a0-040f-4da3-8366-cb0dd3fcf88b","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2016,"title":"C. Eicher. Relaxed highest weight modules from D -modules on the Kashiwara flag scheme. https://arxiv.org/abs/1607.06342 arXiv:1607.06342 [math.RT] , 2016","work_id":"2021aae7-11d0-485a-81f9-271e03f7d0e0","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2011,"title":"C. Eicher. Twisted D -module extensions of local systems on a certain subvariety isomorphic to G _ m ^2 of the affine flag variety of SL _2 . https://arxiv.org/abs/2011.03764 arXiv:2011.03764 [math.AG","work_id":"dbcea37d-1f88-439e-af25-44215b8a607f","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":3,"snapshot_sha256":"71cb863591769176cee557b5478687b5ae21f0834381e8f8fcdae63feb32847a","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"}