Modular tensor categories are rich mathematical structures. They are important in the study of 2D conformal field theory, arising as categories of modules for rational vertex operator algebras. The orbifold construction A-> A^{G}  for a finite group G is a fundamental method for producing new theories from old. In the case the orbifold theory is also rational, the construction of…

Let Q be an orientation of a type A Dynkin diagram. An eta map corresponding to Q is a surjection from the weak order on permutations to a Cambrian lattice (of triangulations of a polygon). We give a new geometric way to construct the Auslander-Reiten quiver of the quiver representations rep(Q). We use it to naturally define…