{"paper":{"title":"Decomposition of Level-1 Representations of D_4^(1) With Respect to its Subalgebra G_2^(1) in the Spinor Construction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Quincy Loney","submitted_at":"2012-08-31T21:17:59Z","abstract_excerpt":"In [FFR] Feingold, Frenkel and Ries gave a spinor construction of the vertex operator para-algebra (abelian intertwining algebra) V = V^0 \\oplus V^1 \\oplus V^2 \\oplus V^3, whose summands are four level-1 irreducible representations of the affine Kac-Moody algebra D_4^(1). The triality group S_3 = < \\sigma,\\tau | \\sigma^3 = 1 = \\tau^2, \\tau\\sigma\\tau = \\sigma^{-1} > in Aut(V) was constructed, preserving V^0 and permuting the V^i, for i=1,2,3. V is (1/2)Z-graded where V^i_n denotes the n-graded subspace of V^i. Vertex operators Y(v,z) for v in V^0_1 represent D_4^(1) on V, while those for which "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0018","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"}