The theory of crystal bases introduced by Kashiwara in [6] 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 [7] he define...

Uncertainty quanti cation and propagation in physical systems appear as a critical path for the improvement of the prediction of their response. Galerkin-type spectral stochastic methods provide a general framework for the numerical simulation of physical models driven by stochastic partial di erential equations. The response is searched in a tensor product space, which is the product of determ...

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...

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 ...

We propose generalized linear models for time or age-time tables of seasonal counts, with the goal of better understanding seasonal patterns in the data. The linear predictor contains a smooth component for the trend and the product of a smooth component (the modulation) and a periodic time series of arbitrary shape (the carrier wave). To model rates, a population offset is added. Twodimensiona...

Let E be an n -dimensional vector space. Then the symmetric group Sym ( ) acts on by permuting elements of a basis and hence r -fold tensor product ? . Bowman, Doty Martin ask, in [1] , whether endomorphism algebra End is cellular. The module permutation for certain Young -set. We shall show that arbitrary -set cellular algebra. determine, terms point stabilisers which appear, when quasi-heredi...

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 $H$.