Title: A vertex model for LLT polynomials and k-tilings of the Aztec diamond
| Speaker: | Andrew Gitlin |
| Affiliation: | UC Berkeley |
| Room/Zoom: | MC5479 or for Zoom link contact Logan Crew or Olya Mandelshtam |
Abstract:
We describe a Yang-Baxter integrable colored vertex model, from which we construct a class of partition functions that equal the LLT polynomials of Lascoux, Leclerc, and Thibon. Using the vertex model formalism, we can prove many properties of these polynomials. We also use the vertex model to study k-tilings (k-tuples of domino tilings) of the Aztec diamond of rank m, where we assign a weight to each k-tiling depending on the number of vertical dominos and the number of "interactions" between the tilings. We compute the generating polynomials of the k-tilings, and prove some combinatorial results about k-tilings in certain limits of the interaction strength.