{"paper":{"title":"From partition identities to a combinatorial approach to explicit Satake inversion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Eunsung Lim, Heekyoung Hahn, Jaebum Sohn, JiSun Huh","submitted_at":"2017-06-10T01:43:53Z","abstract_excerpt":"In this paper, we provide combinatorial proofs for certain partition identities which arise naturally in the context of Langlands' beyond endoscopy proposal. These partition identities motivate an explicit plethysm expansion of $\\mathrm{Sym}^j(\\mathrm{Sym}^kV)$ for $\\mathrm{GL}_2$ in the case $k=3$. We compute the plethysm explicitly for the cases $k=3, 4$. Moreover, we use these expansions to explicitly compute the basic function attached to the symmetric power $L$-function of $\\mathrm{GL}_2$ for these two cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03166","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"}