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We show that the m-cluster category of type A n−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(More)
abstract 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(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 D N with entries which are numbers of matchings between vertices and triangles of corresponding trian-gulations of a punctured disc. For triangulations corresponding to orientations of the Dynkin diagram of type D N , we show that the numbers in the pattern can be interpreted as specialisations of cluster variables in(More)
Let G be a simple algebraic group of classical type over an algebraically closed field k. Let P be a parabolic subgroup of G and let p = Lie P be the Lie algebra of P with Levi decomposition p = l ⊕ u, where u is the Lie algebra of the unipotent radical of P and l is a Levi complement. Thanks to a fundamental theorem of R. W. Richardson ([16]), P acts on u(More)