{"paper":{"title":"On the action of the Steenrod-Milnor operations on the invariants of the general linear groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Nguyen Sum, Nguyen Thai Hoa, Pham Thi Kim Minh","submitted_at":"2017-10-15T12:50:43Z","abstract_excerpt":"Let $p$ be an odd prime number. Denote by $GL_n = GL(n,\\mathbb F_p)$ the general linear group over the prime field $\\mathbb F_p$. Each subgroup of $GL_n$ acts on the algebra $P_n=E(x_1,\\ldots,x_n)\\otimes \\mathbb F_p(y_1,\\ldots,y_n)$ in the usual manner. We grade $P_n$ by assigning $\\dim x_i=1$ and $\\dim y_i=2.$ This algebra is a module over the mod $p$ Steenrod algebra $\\mathcal A_p$. The purpose of the paper is to compute the action of the Steenrod-Milnor operations on the generators of $P_2^{GL_2}$. More precisely, we explicitly determine the action of $St^{(i,j)}$ on the Dickson invariants "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05326","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"}