On Generalized Minors and Quiver Representations

  title={On Generalized Minors and Quiver Representations},
  author={Dylan Rupel and Salvatore Stella and Harold Williams},
  journal={arXiv: Representation Theory},
The cluster algebra of any acyclic quiver can be realized as the coordinate ring of a subvariety of a Kac-Moody group -- the quiver is an orientation of its Dynkin diagram, defining a Coxeter element and thereby a double Bruhat cell. We use this realization to connect representations of the quiver with those of the group. We show that cluster variables of preprojective (resp. postinjective) quiver representations are realized by generalized minors of highest-weight (resp. lowest-weight) group… 
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