Title: From Modeling Fermions to the Puzzle Rule
|Affiliation:||University of Waterloo|
A Knutson-Tao-Woodward puzzle is a tiling of a triangle with certain pieces that have labeled edges. The puzzle rule states that number of puzzles with a given boundary is equal to a Littlewood-Richardson coefficient. I will present a proof of this due to Zinn-Justin which relates the problem to the time evolution of a set of fermions. Transfer matrices describing discrete time steps are applied to elements in the state space of a set of fermions known as Fock space. Repeated applications of the Yang-Baxter equation can "unzip" the transfer matrices, showing they are commutative, which yields the result.
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