A geometric theory of tensor product for glN -crystals is described. In particular, the role of Spaltenstein varieties in the tensor product is explained. As a corollary a direct (non-combinatorial) proof of the fact that the number of irreducible components of a Spaltenstein variety is equal to a Littlewood-Richardson coefficient (i.e. certain tensor product multiplicity) is obtained.

Under some assumptions we prove that the Deligne tensor product of categories of constructible perverse sheaves on pseudomanifolds X and Y is the category of constructible perverse sheaves on X × Y . The Deligne external tensor product functor is identified with the geometrical external tensor product.

Under some assumptions we prove that the Deligne tensor product of categories of constructible perverse sheaves on pseudomanifolds X and Y is the category of constructible perverse sheaves on X × Y . The Deligne external tensor product functor is identified with the geometrical external tensor product.

Abstract An affine de Casteljau type algorithm to compute q−Bernstein Bézier curves is introduced and its intermediate points are obtained explicitly in two ways. Furthermore we define a tensor product patch, based on this algorithm, depending on two parameters. Degree elevation procedure is studied. The matrix representation of tensor product patch is given and we find the transformation matri...

We use a tensor product based multi-linear algebra theory to formulate three-dimensional Hilbert space-filling curves. A 3-D Hilbert space-filling curve is specified as a permutation which rearranges threedimensional n n n data elements stored in the row major order as in C language or the column major order as in FORTRAN language to the order of traversing a 3-D Hilbert space-filling curve. Th...

The theory of tensor products has been used for designing and implementing block recursive numerical algorithms on shared-memory vector multiprocessors such as the Cray-YMP. In this paper, we present an algebraic theory based on tensor products for modeling direct interconnection networks. The development of this model is expected to facilitate the development of a methodology for mapping algor...

We introduced a non-symmetric tensor product of any two states or any two representations of Cuntz-Krieger algebras associated with a certain non-cocommutative comultiplication in previous our work. In this paper, we show that a certain set of KMS states is closed with respect to the tensor product. From this, we obtain formulae of tensor product of type III factor representations of Cuntz-Krie...