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Description

Thrall's problem asks for a combinatorial description of the multiplicities of irreducibles appearing in the higher Lie modules. In this talk, we will give an overview of the problem and describe new approaches involving crystal graphs and dual equivalence graphs. These graph models encode representations of Lie groups and algebras, and are helpful tools for explaining Schur-positivity in type A. Mary Claire has worked on this project together with Joseph Pappe and Anne Schilling, and is excited to share the nice combinatorics encountered while exploring.