https://cnrs.hal.science/hal-03875137Corteel, SylvieSylvieCorteelCNRS - Centre National de la Recherche ScientifiqueGitlin, AndrewAndrewGitlinKeating, DavidDavidKeatingMeza, JeremyJeremyMezaA Vertex Model for LLT PolynomialsHAL CCSD2022[MATH] Mathematics [math]Corteel, Sylvie2022-11-28 11:43:522023-03-24 14:53:292022-11-28 11:43:52enJournal articles10.1093/imrn/rnab1651Abstract We describe a novel Yangâ€“Baxter integrable vertex model. From this vertex model we construct a certain class of partition functions that we show are essentially equal to the LLT polynomials of Lascoux, Leclerc, and Thibon. Using the vertex model formalism, we give alternate proofs of many properties of these polynomials, including symmetry and a Cauchy identity.