{"paper":{"title":"On pro-$p$-Iwahori invariants of $R$-representations of reductive $p$-adic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Guy Henniart, Marie-France Vigneras, Noriyuki Abe","submitted_at":"2017-03-30T09:53:33Z","abstract_excerpt":"Let $F$ be locally compact field with residue characteristic $p$, and $\\mathbf{G}$ a connected reductive $F$-group. Let $\\mathcal{U}$ be a pro-$p$ Iwahori subgroup of $G = \\mathbf{G}(F)$. Fix a commutative ring $R$. If $\\pi$ is a smooth $R[G]$-representation, the space of invariants $\\pi^{\\mathcal{U}}$ is a right module over the Hecke algebra $\\mathcal{H}$ of $\\mathcal{U}$ in $G$.\n  Let $P$ be a parabolic subgroup of $G$ with a Levi decomposition $P = MN$ adapted to $\\mathcal{U}$. We complement previous investigation of Ollivier-Vign\\'eras on the relation between taking $\\mathcal{U}$-invariant"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10384","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"}