Learn More
We show that the m-cluster category of type An−1 is equivalent to a certain geometrically-defined category of diagonals of a regular nm+ 2-gon. This generalises a result of Caldero, Chapoton and Schiffler for m = 1. The approach uses the theory of translation quivers and their corresponding mesh categories. We also introduce the notion of the mth power of a(More)
We construct frieze patterns of type DN with entries which are numbers of matchings between vertices and triangles of corresponding triangulations of a punctured disc. For triangulations corresponding to orientations of the Dynkin diagram of type DN , we show that the numbers in the pattern can be interpreted as specialisations of cluster variables in the(More)
We present an algorithm for computing the dimensions of higher secant varieties of minimal orbits. Experiments with this algorithm lead to many conjectures on secant dimensions, especially of Grassmannians and Segre products. For these two classes of minimal orbits, we also point out a relation between the existence of certain codes and non-defectiveness of(More)
Parabolic subalgebras p of semisimple Lie algebras define a Z-grading of the Lie algebra. If there exists a nilpotent element in the first graded part of g on which the adjoint group of p acts with a dense orbit, the parabolic subalgebra is said to be nice. The corresponding nilpotent element is also called admissible. Nice parabolic subalgebras of simple(More)
Parabolic subalgebras of semi-simple Lie algebras decompose as p = m⊕ n where m is a Levi factor and n the corresponding nilradical. By Richardsons theorem [R], there exists an open orbit under the action of the adjoint group P on the nilradical. The elements of this dense orbits are known as Richardson elements. In this paper we describe a normal form for(More)
We construct frieze patterns of type DN with entries which are numbers of matchings between vertices and triangles of corresponding triangulations of a punctured disc. For triangulations corresponding to orientations of the Dynkin diagram of type DN , we show that the numbers in the pattern can be interpreted as specialisations of cluster variables in the(More)