{"paper":{"title":"On the reductive monoid associated to a parabolic subgroup","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jonathan Wang","submitted_at":"2016-02-23T17:00:13Z","abstract_excerpt":"Let $G$ be a connected reductive group over a perfect field $k$. We study a certain normal reductive monoid $\\overline M$ associated to a parabolic $k$-subgroup $P$ of $G$. The group of units of $\\overline M$ is the Levi factor $M$ of $P$. We show that $\\overline M$ is a retract of the affine closure of the quasi-affine variety $G/U(P)$. Fixing a parabolic $P^-$ opposite to $P$, we prove that the affine closure of $G/U(P)$ is a retract of the affine closure of the boundary degeneration $(G \\times G)/(P \\times_M P^-)$. Using idempotents, we relate $\\overline M$ to the Vinberg semigroup of $G$. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07233","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"}