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Showing 1 to 4 of 4 for “"root lattice"”.
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Combinatorial aspects of root lattices and words
… order. In the first part, the similar sublattices and coincidence site lattices of the root lattice A4 are analysed by means of a particular quaternion algebra. Dirichlet series generating functions are derived, which count the number of similar sublattices, respectively coincidence site …
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Descent Systems, Eulerian Polynomials and Toric Varieties
… the Sn -orbit for a generic weight in the weight lattice of Sn . Therefore the Eulerian polynomials give the Betti numbers for certain smooth toric varieties associated with the permutohedra. In this thesis we derive recurrences for the h-vectors of a family of polytopes generalizing this. The …
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Gromov-Witten theory in dimensions two and three
… quantum product is expressed in terms of an ADE root system canonically associated to G. We generalize the resulting Frobenius manifold to non-simply laced root systems to obtain an n parameter family of algebra structures on the affine root lattice of any root system. Using the Crepant …
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Lattices and Their Applications to Rational Elliptic Surfaces
… namely the Mordell-Weil Group, Mordell-Weil Lattice, and another lattice which will be called the Shioda Lattice. It will begin with a brief overview of rational elliptic surfaces, followed by a discussion of lattices, root systems and Dynkin diagrams. Known results of several authors will …