The Kneser-Hecke-operator is a linear operator defined on the complex vector space spanned by the equivalence classes of a family of self-dual codes of fixed length. It maps a linear self-dual code C over a finite field to the formal sum of the equivalence classes of those self-dual codes that intersect C in a codimension 1 subspace. The eigenspaces of this self-adjoint linear operator may be d...

In this work we study the duality for a general multiobjective optimization problem. Considering, first, a scalar problem, different duals using the conjugacy approach are presented. Starting from these scalar duals, we introduce six different multiobjective dual problems to the primal one, one depending on certain vector parameters. The existence of weak and, under certain conditions, of stron...

Self-dual 2-forms in D = 2n dimensions are characterised by an eigenvalue criterion. The equivalence of various definitions of selfduality is proven. We show that the self-dual 2-forms determine a n − n + 1 dimensional manifold S2n and the dimension of the maximal linear subspaces of S2n is equal to the Radon-Hurwitz number of linearly independent vector fields on the sphere S. The relation bet...

We study N = 1 supersymmetric Spin(10) chiral gauge theories with a single spinor representation and N vector representations. We present a dual description in terms of an N = 1 supersymmetric SU(N − 5) chiral gauge theory with a symmetric tensor, one fundamental and N antifundamental representations. The Spin(10) theory with N = 0 breaks supersymmetry at strong coupling; we study how this aris...

The braid group Bn maps homomorphically into the TemperleyLieb algebra TLn. It was shown by Zinno that the homomorphic images of simple elements arising from the dual presentation of the braid group Bn form a basis for the vector space underlying the Temperley-Lieb algebra TLn. In this paper, we establish that there is a dual presentation of Temperley-Lieb algebras that corresponds to the dual ...

1.2. Let E be a Euclidean vector space, Φ ⊂ E∗ a root system. Denote Q ⊂ h∗ the root lattice, and P ⊂ h∗ the weight lattice. Let Q∨ ⊂ E be the lattice generated by the coroots α∨, α ∈ Φ, the coroot lattice is dual to the weight lattice P ⊂ h∗, and P∨ ⊂ E the dual weight lattice, which is dual to the root lattice Q. Let H = HomZ(P,C) = Q∨ ⊗Z C∗ be the complex algebraic torus with Lie algebra h =...

We present the first anonymous hierarchical identity based encryption (HIBE) scheme using Type-3 pairings with adaptive security based on standard assumptions. Previous constructions of anonymous HIBE schemes did not simultaneously achieve all these features. The new construction uses dual pairing vector spaces using an identity hash earlier used by Boneh, Boyen and Goh. The proof of security f...

Null designs on the poset of dual polar spaces are considered. A poset of dual polar spaces is the set of isotropic subspaces of a finite vector space equipped with a nondegenerate bilinear form, ordered by inclusion. We show that the minimum number of isotropic subspaces to construct a nonzero null t-design is Qt i=0(1 + q ) for the types BN , DN , whereas for the case of type CN , more isotro...

Remark. It is also possible to define tensors over a complex vector space (with no essential modifications in the definitions and results below, except that the special Euclidean case no longer applies). This is important in many other applications (including complex manifolds), but will not be considered here. 1.1. The dual space. Let V ∗ = hom(V ;R) be the dual of V , i.e. the vector space of...

We derive a new representation for a function as a linear combination of local correlation kernels at optimal sparse locations and discuss its relation to PCA, regularization, sparsity principles and Support Vector Machines. We also discuss its Bayesian interpretation and justiication. We rst review previous results for the approximation of a function from discrete data (Girosi, 1998) in the co...