{"paper":{"title":"The Second Main Theorem Vector for the modular regular representation of $C_2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"David L. Wehlau, H.E.A. Campbell","submitted_at":"2013-08-16T20:09:12Z","abstract_excerpt":"We study the ring of invariants for a finite dimensional representation $V$ of the group $C_2$ of order 2 in characteristic $2$. Let $\\sigma$ denote a generator of $C_2$ and $\\{x_1,y_1 \\dots, x_m,y_m\\}$ a basis of $V^*$. Then $\\sigma(x_i) = x_i$, and $\\sigma(y_i) = y_i + x_i$. To our knowledge, this ring (for any prime $p$) was first studied by David Richman in 1990. He gave a first main theorem for $(V_2, C_2)$, that is, he proved that the ring of invariants when $p=2$ is generated by $\\{x_i, N_i = y_i^2 + x_iy_i, tr(A) | 2 \\le |A| \\le m\\}$ where $A \\subset \\{0,1\\}^m$, $y^A = y_1^{a_1} y_2^{a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3710","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"}