{"paper":{"title":"On the saturation conjecture for $\\operatorname{Spin}(2n)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Joshua Kiers","submitted_at":"2018-04-24T19:46:34Z","abstract_excerpt":"In this paper we examine the saturation conjecture on decompositions of tensor products of irreducible representations for complex semisimple algebraic groups of type $D$ (the even \\emph{spin} groups: Spin$(2n)$ for $n\\ge 4$ an integer), extending work done by Kumar-Kapovich-Millson on Spin(8). Our main theorem asserts that the saturation conjecture holds for Spin(10) and Spin(12): for all triples of dominants weights $\\lambda,\\mu,\\nu$ such that $\\lambda+\\mu+\\nu$ is in the root lattice, and for any $N>0$, $$ \\left(V(\\lambda)\\otimes V(\\mu)\\otimes V(\\nu)\\right)^G \\ne 0 $$ if and only if $$ \\left"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09229","kind":"arxiv","version":3},"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"}