{"paper":{"title":"Littelmann path model for geometric crystals, Whittaker functions on Lie groups and Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RT"],"primary_cat":"math.PR","authors_text":"Reda Chhaibi","submitted_at":"2013-02-04T23:34:23Z","abstract_excerpt":"Generally speaking, this thesis focuses on the interplay between the representations of Lie groups and probability theory. It subdivides into essentially three parts.\n  In a first rather algebraic part, we construct a path model for geometric crystals in the sense of Berenstein and Kazhdan, for complex semi-simple Lie groups. We will mainly describe the algebraic structure, its natural morphisms and parameterizations. The theory of total positivity will play a particularly important role.\n  Then, we anticipate on the probabilistic part by exhibiting a canonical measure on geometric crystals. I"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0902","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"}