{"paper":{"title":"Hypoelliptic heat kernel on nilpotent Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.PR","math.RT"],"primary_cat":"math.DG","authors_text":"Malva Asaad, Maria Gordina","submitted_at":"2015-05-15T00:44:39Z","abstract_excerpt":"The starting point of our analysis is an old idea of writing an eigenfunction expansion for a heat kernel considered in the case of a hypoelliptic heat kernel on a nilpotent Lie group $G$. One of the ingredients of this approach is the generalized Fourier transform. The formula one gets using this approach is explicit as long as we can find all unitary irreducible representations of $G$. In the current paper we consider an $n$-step nilpotent Lie group $G_{n}$ as an illustration of this technique. First we apply Kirillov's orbit method to describe these representations for $G_{n}$. This allows "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03928","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"}