{"paper":{"title":"When is the ring of $T$ invariants of the homogeneous coordinate ring of $G/B$ a polynomial algebra- connection with the Coxeter elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"B. Narasimha Chary, Santosha Kumar Pattanayak, S. Senthamarai Kannan","submitted_at":"2011-10-11T07:28:34Z","abstract_excerpt":"In this article, we prove that for any indecomposable dominant character of a maximal torus $T$ of a simple adjoint group $G$ such that there is a Coxeter element $w \\in W$ for which $X(w)^{ss}_T(\\mathcal L_\\chi) \\neq \\emptyset$. If further, for any dominant character $\\chi_1$ of $T$ such that $\\chi_1\\lneqq \\chi$ with respect to the dominant ordering, $dim(H^0(G/B, \\mathcal L_{\\chi_1})^T) < dim (H^0(G/B, \\mathcal L_\\chi)^T)$, then the graded algebra $\\oplus_{d \\in \\mathbb Z_{\\geq 0}}H^0(G/B, \\mathcal L_\\chi^{\\otimes d})^T$ is a polynomial ring in $r$ variables where $r\\geq 2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2291","kind":"arxiv","version":2},"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"}