{"paper":{"title":"Geometric conditions for $\\square$-irreducibility of certain representations of the general linear group over a non-archimedean local field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alberto Minguez, Erez Lapid","submitted_at":"2016-05-27T08:55:07Z","abstract_excerpt":"Let $\\pi$ be an irreducible, complex, smooth representation of $GL_n$ over a local non-archimedean (skew) field. Assuming $\\pi$ has regular Zelevinsky parameters, we give a geometric necessary and sufficient criterion for the irreducibility of the parabolic induction of $\\pi\\otimes\\pi$ to $GL_{2n}$. The latter irreducibility property is the $p$-adic analogue of a special case of the notion of \"real representations\" introduced by Leclerc and studied recently by Kang-Kashiwara-Kim-Oh (in the context of KLR or quantum affine algebras). Our criterion is in terms of singularities of Schubert variet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08545","kind":"arxiv","version":5},"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"}