{"paper":{"title":"Branching laws for the Steinberg representation: the rank 1 case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Paul Broussous","submitted_at":"2018-10-16T10:07:03Z","abstract_excerpt":"Let $G/H$ be a reductive symmetric space over a $p$-adic field $F$, the algebraic groups $G$ and $H$ being assumed semisimple of relative rank $1$. One of the branching problems for the Steinberg representation $\\St_G$ of $G$ is the determination of the dimension of the intertwining space ${\\rm Hom}_H (\\St_G ,\\pi )$, for any irreducible representation $\\pi$ of $H$. In this work we do not compute this dimension, but show how it is related to the dimensions of some other intertwining spaces ${\\rm Hom}_{K_i} ({\\tilde \\pi} ,1)$, for a certain finite family $K_i$, $i=1,...,r$, of anisotropic subgro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.06910","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"}