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Horizontal-strip LLT polynomials

Algebra & Discrete Mathematics

Speaker: Foster Tom, UC Berkeley
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Location: MSB 1147 + Zoom (livestream)
Start time: Mon, Nov 29 2021, 11:00AM

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.