{"paper":{"title":"Non-Archimedean Whittaker functions as characters: a probabilistic approach to the Shintani-Casselman-Shalika formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.NT","math.PR"],"primary_cat":"math.RT","authors_text":"Reda Chhaibi","submitted_at":"2014-09-16T13:00:07Z","abstract_excerpt":"For a reductive group $G$ over a non-Archimedean local field (e.g $GL_n( \\mathbb{Q}_p )$ ), Jacquet's Whittaker function is essentially proportional to a character of an irreducible representation of the Langlands dual group $G^\\vee( \\mathbb{C} )$ ( a Schur function if $G = GL_n( \\mathbb{Q}_p )$). We propose a probabilistic approach to this claim, known as the Shintani-Casselman-Shalika formula, when the group $G$ has at least one minuscule cocharacter in the coweight lattice.\n  Our presentation goes along the following lines. Thanks to a minuscule random walk $W^{(z)}$ on the coweight lattice"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4615","kind":"arxiv","version":3},"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"}