{"paper":{"title":"Krawtchouk polynomials, the Lie algebra $\\mathfrak{sl}_2$, and Leonard pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Kazumasa Nomura, Paul Terwilliger","submitted_at":"2012-01-08T17:55:37Z","abstract_excerpt":"A Leonard pair is a pair of diagonalizable linear transformations of a finite-dimensional vector space, each of which acts in an irreducible tridiagonal fashion on an eigenbasis for the other one. In the present paper we give an elementary but comprehensive account of how the following are related: (i) Krawtchouk polynomials; (ii) finite-dimensional irreducible modules for the Lie algebra ${\\mathfrak{sl}_2}$; (iii) a class of Leonard pairs said to have Krawtchouk type. Along the way we obtain elementary proofs of some well-known facts about Krawtchouk polynomials, such as the three-term recurr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1645","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"}