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Summary: Applications of dual equivalence graphs
Sami Assaf
University of Pennsylvania
sassaf@math.mit.edu
S. Assaf - Applications of dual equivalence graphs p.1/22
Outline
I. Graphs on tableaux
· Crystal graphs
· Dual equivalence graphs
II. Symmetric functions
· Schur positivity from graphs
· LLT and Macdonald polynomials
III. Representation Theory
· Weyl groups acting on 0-weight spaces
· From crystal graphs to dual equivalence graphs
S. Assaf - Applications of dual equivalence graphs p.2/22
I. Graphs on Tableaux
S. Assaf - Applications of dual equivalence graphs p.3/22
Crystal graphs
In 1990, Kashiwara introduced crystal bases for representations of
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