{"paper":{"title":"Equivariant $K$-theory of regular compactifications: further developments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"V. Uma","submitted_at":"2014-09-11T15:05:15Z","abstract_excerpt":"In this article we describe the $\\tG\\times \\tG$-equivariant $K$-ring of $X$, where $\\tG$ is a {\\it factorial} cover of a connected complex reductive algebraic group $G$, and $X$ is a regular compactification of $G$. Furthermore, using the description of $K_{\\tG\\times \\tG}(X)$, we describe the ordinary $K$-ring $K(X)$ as a free module of rank the cardinality of the Weyl group, over the $K$-ring of a toric bundle over $G/B$, with fibre the toric variety $\\bar{T}^{+}$, associated to a smooth subdivision of the positive Weyl chamber. This generalizes our previous work on the wonderful compactifica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3467","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"}