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"Quiver" is the word used for "directed graph" in some parts of representation theory. The main reason to use the term quiver is to indicate an interest in considering representations of the quiver.
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Irreducibility of the F-polynomial of an indecomposable quiver representation
Question. Is the $F$-polynomial of an indecomposable quiver representation irreducible?
Here the $F$-polynomial is the generating function of the Euler characteristics of quiver Grassmannians, …