BGP-reflection functors and cluster combinatorics ∗

  title={BGP-reflection functors and cluster combinatorics ∗},
  author={Bin Zhu},
We define Bernstein-Gelfand-Ponomarev reflection functors in the cluster categories of hereditary algebras. They are triangle equivalences which provide a natural quiver realization of the " truncated simple reflections " on the set of almost positive roots Φ ≥−1 associated to a finite dimensional semisimple Lie algebra. Combining with the tilting theory in cluster categories developed in [4], we give a unified interpretation via quiver representations for the generalized associahedra… CONTINUE READING