One-skeleton galleries and cell combinatorics in type A

We describe the image of a cell in the Bialynicki-Birula decomposition of Gaussent and Littelmann's Bott-Samelson type variety, which is a desingularization of an affine Schubert variety, in type A for two particular cases. In the first case, we take a one-skeleton gallery, which is completely included in the dominant Weyl chamber. We can show, that the closure of the image of the cells associated to galleries, that belong to certain parts of the associated crystal, are in fact MV-cycles. In the second case we take a gallery of type N\omega_1, which is completely included in the dominant Weyl chamber. We generalize the notion of a Young tableau and use the 1:1 correspondance between tableaux and one-skeleton galleries to analyze, how the associated cells behave under the bumping algorithm. Finally, we can show that if and only if we take two words, equivalent under the Knuth relations, then the closure of the images of the cells associated to the galleries coming from these word, are the same. In addition, this closure is an MV-cycle. This allows a geometric interpretation of the combinatoric Knuth relations in the plactic monoid

Hermitian Maass lift for General Level

For an imaginary quadratic field $K$ of discriminant $-D$, let $\chi = \chi_K$ be the associated quadratic character. We will show that the space of special hermitian Jacobi forms of level $N$ is isomorphic to the space of plus forms of level $DN$ and nebentypus $\chi$ (the hermitian analogue of Kohnen's plus space) for any integer $N$ prime to $D$. This generalizes the results of Krieg from $N = 1$ to arbitrary level. Combining this isomorphism with the recent work of Berger and Klosin and a modification of Ikeda's construction we prove the existence of a lift from the space of elliptic modular forms to the space of hermitian modular forms of level $N$ which can be viewed as a generalization of the classical hermitian \Maass lift to arbitrary level

Growth of Asian Regional Trade and Income Convergence: Evidence from ASEAN+3 Based on Extended Helpman-Krugman Hypothesis and Flexible Modelling Approach

In earlier cross-sectional gravity-theory reports (see for example Frankel and Romer, 1999), empirical modelling evidence lends support to the hypothesis of ‘trade causes growth’. In our time-series study on trade-growth causation for a new Asian regionalism (namely ASEAN+3), the hypothesis was also confirmed (Tran Van Hoa, 2002c). A number of benchmark models have also been proposed to find out what causes trade (for a brief survey, see Baier and Bergstrand, 2001), but specific research on income convergence and Asian or more specifically ASEAN+3 trade is still scarce or even non-existent. The paper focuses on studying the growth of ASEAN+3 bilateral trade in the volatile period 1968-2000 and, using an extended Helpman-Krugman (1985) function-free model and World Bank national account and CHELEM trade data, tests the impact of convergence on this trade. Surprisingly, this convergence is found plausible but statistically insignificant and ASEAN output growth and crises are principal determinants of the trade flows between the East Asia 3 and ASEAN.New Asian Regionalism, Free Trade Agreement, ASEAN, ASEAN+3, Trade and Growth, Crises, Convergence Theory, Gravity Theory, Causality, Economic Modelling, Estimation Methods, Economic and Trade Policy

Recent Significant Advances in Estimating and Forecasting Theories and Economic Modelling: With Applications to Asian Investment Studies.

The paper presents the basics of a new and flexible approach to statistically modelling the activities of multi-sectoral economies (Tran Van Hoa, 1992) and applies it to study investment in five major East Asian countries (ie, China, Indonesia, Korea, Malaysia and Thailand) during the period 1970-1993 using recent World Bank databases. The approach dominates the computable general equilibrium method in its data-consistent structure.ECONOMIC MODELS ; EVALUATION ; FORECASTS ; INVESTMENTS