The theory of crystal bases introduced by Kashiwara in [4] to study the category of integrable representations of quantized Kac–Moody Lie algebras has been a major development in the combinatorial approach to representation theory. In particular Kashiwara defined the tensor product of crystal bases and showed that it corresponded to the tensor product of representations. Later, in [5] he define...

A q-plate is a stratified medium composed of a uniaxial nematic liquid crystal with an inhomogeneous orientation of the optical axis possessing a topological charge q, which looks promising as a switching device. This work reports an approach to diagonalizing the dielectric tensor in q-plates, giving a detailed study of nontrivial tensor coordinate transformations. The relationship between the ...

The forgotten topological index is defined as sum of third power of degrees. In this paper, we compute some properties of forgotten index and then we determine it for some classes of product graphs.

EXTENT M an EXpert system for TENsor product formula Translation. In this paper we present a programming environment for automattc generation of parallel/vector programs from tensor product formulas. A tensor (Kronecker) product based programming methodology is used for deszgning high performance programs on vartous architectures. In thts programming methodology, block recurstve algordhms such ...

A bi-unitary connection in subfactor theory of Jones producing a finite depth gives 4-tensor appearing recent work Bultinck-Mariena-Williamson-Sahinoglu-Haegemana-Verstraete on 2-dimensional topological order and anyons. In their work, they have special projection called projector matrix product operator. We prove that the range this length k is naturally identified with k-th higher relative co...

Quantum computers will work by evolving a high tensor power of a small (e.g. two) dimensional Hilbert space by local gates, which can be implemented by applying a local Hamiltonian H for a time t. In contrast to this quantum engineering, the most abstract reaches of theoretical physics has spawned “topological models” having a finite dimensional internal state space with no natural tensor produ...

In this paper we define an order structure on the $p$-operator projective tensor product of Herz algebras and we show that the canonical isometric isomorphism between $A_p(Gtimes H)$ and $A_p(G)widehat{otimes}^p A_p(H)$ is an order isomorphism for amenable groups $G$ and $H$.

We introduce a version of Voiculescu-Brown approximation entropy for isometric automorphisms of Banach spaces and develop within this framework the connection between dynamics and the local theory of Banach spaces discovered by Glasner and Weiss. Our fundamental result concerning this contractive approximation entropy, or CA entropy, characterizes the occurrence of positive values both geometri...