Young wall realization of crystal graphs for U_q(C_n^{(1)})

We give a realization of crystal graphs for basic representations of the quantum affine algebra U_q(C_n^{(1)}) using combinatorics of Young walls. The notion of splitting blocks plays a crucial role in the construction of crystal graphs

Crystal bases for quantum affine algebras and combinatorics of Young walls

In this paper, we give a realization of crystal bases for quantum affine algebras using some new combinatorial objects which we call the Young walls. The Young walls consist of colored blocks with various shapes that are built on the given ground-state wall and can be viewed as generalizations of Young diagrams. The rules for building Young walls and the action of Kashiwara operators are given explicitly in terms of combinatorics of Young walls. The crystal graphs for basic representations are characterized as the set of all reduced proper Young walls. The characters of basic representations can be computed easily by counting the number of colored blocks that have been added to the ground-state wall

Relative Backwardness and Technological Catching Up with Scale Effects

This paper theoretically and empirically analyzes the sources of the observed pattern that the levels and growth rates of technology are different across countries. The model is extended version of endogenous growth models with catching up model which is formulated by the relative backwardness hypothesis and the adoption capacity. The relative backwardness hypothesis states that the backward countries attain a high productivity growth rate because adopting advanced technologies is easier and less costly than innovation, Thus, the technologically less advanced countries tend to grow faster than technologically leading countries. A necessary condition, in order that the laggard countries might be able to take advantage of the available technology, is the well-developed capacity, ``Adoption capacity'', to adopt the superior technology. This is determined by policy variables that are conducive to technology adoption. The catching up theory states that technological catching up is strongest in countries that are not only technologically backward but also in those countries which have policy determinants conducive to technology adoption. Theoretically, it is shown that the steady state growth rate of technology is determined by population growth rate while the steady state relative backwardness depends on the adoption capacity, the productivity in the R&D sector, and the relative human capital stock. The empirical relevance of the catching up theory is investigated as well. The empirical results support the formalized catching up theory by showing the significant role which policy determinants conducive to technological adoption play. The robust role of scale effects in explaining technological catching up is also shown. Further, the speeds of technological catching up are estimated to be around 2 percent.