Speaker:  Foster Tom  (MIT)

Title:  Horizontal-strip LLT polynomials

Abstract:

Lascoux, Leclerc, and Thibon defined a remarkable family of symmetric functions that are q-deformations of products of skew Schur functions. These LLT polynomials $G_{\lambda}(x;q)$ can be indexed by a tuple $\lambda$ of skew diagrams. When each skew diagram is a row, we define a weighted graph $\Pi(\lambda)$. We show that a horizontal-strip LLT polynomial is determined by this weighted graph. When $Pi(\lambda)$ has no triangles, we establish a combinatorial Schur expansion of $G_{\lambda}(x;q)$. We also explore a connection to extended chromatic symmetric functions.