{"paper":{"title":"Lie powers of the natural module for GL(2,K)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Karin Erdmann, Marianne Johnson","submitted_at":"2011-05-23T17:59:30Z","abstract_excerpt":"In recent work of R. M. Bryant and the second author a (partial) modular analogue of Klyachko's 1974 result on Lie powers of the natural $\\rm{GL}(n,K)$ was presented. There is was shown that nearly all of the indecomposable summands of the $r$th tensor power also occur up to isomorphism as summands of the $r$th Lie power provided that $r\\neq p^m$ and $r \\neq 2p^m$, where $p$ is the characteristic of $K$. In the current paper we restrict attention to ${\\rm GL}(2,K)$ and consider the missing cases where $r = p^m$ and $r = 2p^m$. In particular, we prove that the indecomposable summand of the $r$t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4576","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"}