{"paper":{"title":"Blocks of the Grothendieck ring of equivariant bundles on a finite group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"C\\'edric Bonnaf\\'e","submitted_at":"2014-05-22T20:36:35Z","abstract_excerpt":"If $G$ is a finite group, the Grothendieck group ${\\mathbf{K}}\\_G(G)$ of the category of $G$-equivariant ${\\mathbb{C}}$-vector bundles on $G$ (for the action of $G$ on itself by conjugation) is endowed with a structure of (commutative) ring. If $K$ is a sufficiently large extension of ${\\mathbb{Q}}\\_{\\! p}$ and ${\\mathcal{O}}$ denotes the integral closure of ${\\mathcal{Z}}\\_{\\! p}$ in $K$, the $K$-algebra $K{\\mathbf{K}}\\_G(G)=K \\otimes\\_{\\mathbb{Z}} {\\mathbf{K}}\\_G(G)$ is split semisimple. The aim of this paper is to describe the ${\\mathcal{O}}$-blocks of the ${\\mathcal{O}}$-algebra ${\\mathcal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5903","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"}