{"paper":{"title":"Classification of symmetric pairs with discretely decomposable restrictions of (g,K)-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Toshiyuki Kobayashi, Yoshiki Oshima","submitted_at":"2012-02-26T11:25:41Z","abstract_excerpt":"We give a complete classification of reductive symmetric pairs (g, h) with the following property: there exists at least one infinite-dimensional irreducible (g,K)-module X that is discretely decomposable as an (h,H \\cap K)-module.\n  We investigate further if such X can be taken to be a minimal representation, a Zuckerman derived functor module A_q(\\lambda), or some other unitarizable (g,K)-module.\n  The tensor product $\\pi_1 \\otimes \\pi_2$ of two infinite-dimensional irreducible (g,K)-modules arises as a very special case of our setting. In this case, we prove that $\\pi_1 \\otimes \\pi_2$ is di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5743","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"}