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Sortable elements for quivers with cycles.

Reading, Nathan; Speyer, David E. — 2010

The Electronic Journal of Combinatorics [electronic only]

Cambrian fans

Nathan Reading; David E. Speyer — 2009

Journal of the European Mathematical Society

For a finite Coxeter group $W$ and a Coxeter element $c$ of $W$ ; the $c$ -Cambrian fan is a coarsening of the fan defined by the reflecting hyperplanes of $W$ . Its maximal cones are naturally indexed by the $c$ -sortable elements of $W$ . The main result of this paper is that the known bijection cl $_{c}$ between $c$ -sortable elements and $c$ -clusters induces a combinatorial isomorphism of fans. In particular, the $c$ -Cambrian fan is combinatorially isomorphic to the normal fan of the generalized associahedron for $W$ . The rays...

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