{"paper":{"title":"Dimensions of Higher Extensions for SL_2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alison E. Parker, Karin Erdmann, Keith C. Hannabuss","submitted_at":"2012-10-09T10:57:36Z","abstract_excerpt":"We analyse the recursive formula found for various Ext groups for $\\SL_2(k)$, $k$ a field of characteristic $p$, and derive various generating functions for these groups. We use this to show that the growth rate for the cohomology of $\\SL_2(k)$ is at least exponential. In particular, $\\max \\{\\dim \\Ext^i_{\\SL_2(k)}(k, \\Delta(a))\\mid a,i \\in \\N \\}$ has (at least) exponential growth for all $p$. We also show that $\\max \\{\\dim \\Ext^i_{\\SL_2(k)}(k, \\Delta(a))\\mid a\\in \\N \\}$ for a fixed $i$ is bounded."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2557","kind":"arxiv","version":2},"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"}