{"paper":{"title":"On representations of GL(n) distinguished by GL(1)*GL(n-1) over a quaternion division algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Hariom Sharma, Mahendra Kumar Verma, Prem Dagar","submitted_at":"2026-06-04T19:56:49Z","abstract_excerpt":"Let $D$ be a quaternion division algebra over a non-Archimedean local field $F$ of characteristic zero, and let $G_n=GL_n(D)$. Let $H_{1,n-1}$ denote the subgroup of $G_n$ consisting of block-diagonal matrices of the form $diag(g_1,g_2)$, where $g_1\\in G_1$ and $g_2\\in G_{n-1}$. In this article, we formulate a conjectural classification of irreducible smooth $H_{1,n-1}$-distinguished representations of $G_n$ for $n>2$. We prove this conjecture in the cases $n=3$ and $n=4$. When $n=2$, the results are well known due to the contributions by various authors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06683","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.06683/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}