A Vertex Model for LLT Polynomials

Sylvie Corteel (1) , Andrew Gitlin , David Keating , Jeremy Meza

1 CNRS - Centre National de la Recherche Scientifique

Abstract We describe a novel Yang–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.

Domaines: Mathématiques [math]

Sylvie Corteel, Andrew Gitlin, David Keating, Jeremy Meza. A Vertex Model for LLT Polynomials. International Mathematics Research Notices, 2022, 2022 (20), pp.15869-15931. ⟨10.1093/imrn/rnab165⟩. ⟨hal-03875137⟩