{"paper":{"title":"Some conditions for descent of line bundles to GIT quotients $(G/B \\times G/B \\times G/B)//G$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Nathaniel Bushek","submitted_at":"2016-11-29T20:08:57Z","abstract_excerpt":"We consider the descent of line bundles to GIT quotients of products of flag varieties. Let $G$ be a simple, connected, algebraic group over $\\mathbb{C}$. We fix a Borel subgroup $B$ and consider the diagonal action of $G$ on the projective variety $X = G/B \\times G/B \\times G/B$. For any triple $(\\lambda, \\mu, \\nu)$ of dominant regular characters there is a $G$-equivariant line bundle $\\mathcal{L}$ on $X$. Then, $\\mathcal{L}$ is said to descend to the GIT quotient $\\pi:[X(\\mathcal{L})]^{ss} \\rightarrow X(\\mathcal{L})//G$ if there exists a line bundle $\\hat{\\mathcal{L}}$ on $X(\\mathcal{L})//G$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09818","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"}