{"paper":{"title":"$K$-type multiplicities in degenerate principal series via Howe duality","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Andrew Frohmader, Jeb F. Willenbring, Mark Colarusso, William Q. Erickson","submitted_at":"2025-02-26T19:11:52Z","abstract_excerpt":"Let $K$ be one of the complex classical groups ${\\rm O}_k$, ${\\rm GL}_k$, or ${\\rm Sp}_{2k}$. Let $M \\subseteq K$ be the block diagonal embedding ${\\rm O}_{k_1} \\times \\cdots \\times {\\rm O}_{k_r}$ or ${\\rm GL}_{k_1} \\times \\cdots \\times {\\rm GL}_{k_r}$ or ${\\rm Sp}_{2k_1} \\times \\cdots \\times {\\rm Sp}_{2k_r}$, respectively. By using Howe duality and seesaw reciprocity as a unified conceptual framework, we prove a formula for the branching multiplicities from $K$ to $M$ which is expressed as a sum of generalized Littlewood-Richardson coefficients, valid within a certain stable range. By viewing"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.19505","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/2502.19505/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"}