Combinatorial realizations of crystals via torus actions on quiver varieties

Consider Kashiwara's crystal associated to a highest weight representation of a symmetric Kac-Moody algebra. There is a geometric realization of this object using Nakajima's quiver varieties, but in many particular cases it can also be realized by elementary combinatorial methods. Here we propose a framework for extracting combinatorial realizations from the geometric picture: We construct certain torus actions on the quiver varieties and use Morse theory to index the irreducible components by connected components of the subvariety of torus fixed points. We then discuss the case of affine sl(n). There the fixed point components are just points, and are naturally indexed by multi-partitions. There is some choice in our construction, leading to a family of combinatorial models for each highest weight crystal. Applying this construction to the crystal of the fundamental representation recovers a family of combinatorial realizations recently constructed by Fayers. This gives a more conceptual proof of Fayers' result as well as a generalization to higher level. We also discuss a relationship with Nakajima's monomial crystal.Comment: 23 pages, v2: added Section 8 on monomial crystals and some references; v3: many small correction

"Innovation Versus Diffusion: Determinants of Productivity Growth Among Japanese Firms"

This paper presents a model of firm-level productivity growth that distinguishes between innovation and technology diffusion, and then applies the model to a large-scale data set of Japanese manufacturing and non-manufacturing firms between 1994 and 2000. We find both innovation and diffusion are important factors in firm-level productivity growth. Results also suggest that innovation comes not only directly from R&D activities, but also indirectly from patent purchases and imports. Previously, patent purchases and imports were considered as sources of technology diffusion rather than innovation. In fact, we find patent purchases are more effective in this regard than R&D expenditure.

"Productivity Convergence at the Firm Level"

Productivity convergence among countries has been investigated extensively with mixed results. This paper extends the analysis to the firm level to shed light on the debate of convergence or non-convergence. We find productivity convergence among firms widely in Japan, in both manufacturing industries and non-manufacturing ones. We obtain these results taking explicit account of exiting firms as a source of selection biases. The convergence rate is much faster among firms than countries. We also find that there are substantial differences among industries in the convergence speed. IT industries that heavily rely on technological progress show faster rates of convergence.

"Does Natural Selection Mechanism Still Work in Severe Recessions? --]Examination of the Japanese Economy in the 1990s ---"

This paper investigates whether or not the natural selection mechanism (NSM) of economic Darwinism works in severe recessions. Although standard firm models imply the importance of NSM in an economy by showing firm's rational behavior on entry, surviv-ing, and exit leads to macro-level TFP growth, there is almost no evidence to demonstrate NSM works even in severe recessions and depressions. Based on micro data of the Basic Survey of Japanese Business Structure and Activities (BSJBSA) by Ministry of Economy, Trade and Industry, we construct a comprehensive firm-level panel dataset for Japan from 1994 to 1998, especially designed for the analysis of a firm's entry, survival, and exit and its relationship with TFP. Empirical results show that efficient firms in terms of TFP quit while inefficient ones survived in the banking-crisis period of 1996-1997. Besides, this phenomenon is mainly observed for new entrants and contributes substantially to a fall in macro TFP after 1996. These facts strongly suggest malfunctioning of NSM in severe recessions.

Josephson Effects in Double-Layer Quantum Hall States

Under quite plausible assumptions on double-layer quantum Hall states with strong interlayer correlation, we show in general framwork that coherent tunneling of a single electron between two layers is possible. It yields Josephson effects with unit charge tunneling. The origin is that Halperin states in the quantum Hall states are highly degenerate in electron number difference between two layers in the absence of electrons tunneling.Comment: 9 Pages, Revtex Inpress Int.J.Mod.Phys.

Weight Vectors of the Basic A_1^(1)-Module and the Littlewood-Richardson Rule

The basic representation of \A is studied. The weight vectors are represented in terms of Schur functions. A suitable base of any weight space is given. Littlewood-Richardson rule appears in the linear relations among weight vectors.Comment: February 1995, 7pages, Using AMS-Te

Single Pion Measurement Capabilities at SciBooNE

The precise knowledge of the single pion production cross-section of neutrino around the ~1 GeV energy region is an essential ingredient in the interpretation of neutrino oscillation experiments. The unique opportunities and prospects of single pion measurements at SciBooNE are described.Comment: Proceedings of the 5th International Workshop on Neutrino-Nucleus Interactions in the Few-GeV Region (NuInt07), Batavia, Illinois, 30 May - 3 Jun 200

Specific heat evidence for two-gap superconductivity in ternary-iron silicide Lu2_{2}Fe3_{3}Si5_{5}

We report low-temperature specific heat studies on single-crystalline ternary-iron silicide superconductor Lu$_{2}$Fe$_{3}$Si$_{5}$ with$T_c$ = 6.1 K down to $\sim T_c/20$. We confirm a reduced normalized jump in specific heat at $T_c$, and find that the specific heat divided by temperature $C/T$ shows sudden drop at $\sim T_c/5$ and goes to zero with further decreasing temperature. These results indicate the presence of two distinct superconducting gaps in Lu$_{2}$Fe$_{3}$Si$_{5}$, similar to a typical two-gap superconductor MgB$_{2}$. We also report Hall coefficients, band structure calculation, and the anisotropy of upper critical fields for Lu$_{2}$Fe$_{3}$Si$_{5}$, which support the anisotropic multiband nature and reinforce the existence of two superconducting gaps in Lu$_{2}$Fe$_{3}$Si$_{5}$.Comment: 5 pages, 5 figure

Infrared Features of the Landau Gauge QCD

The infrared features of Landau gauge QCD are studied by the lattice simulation of $\beta=6.0, 16^4, 24^4, 32^4$ and $\beta=6.4, 32^4, 48^4$. We adopt two definitions of the gauge field; 1) $U-$linear 2) $\log U$ and measured the gluon propagator and ghost propagator. Infrared singularity of the gluon propagator is less than that of tree level result but the gluon propagator at 0 momentum remains finite. The infrared singularity of ghost propagator is stronger than the tree level. The QCD running coupling measured by using the gluon propagator and the ghost propagator has a maximum $\alpha_s(p)\simeq 1$ at around $p=0.5GeV$ and decreases as $p$ approaches 0. The data are analyzed in use of formula of the principle of minimal sensitivity(PMS), the effective charge method and the contour-improved perturbation method, which suggest necessity of the resummation of perturbation series in the infrared region together with existence of the infrared fixed point. Kugo-Ojima parameter saturates at about -0.8 in contrast to the theoretically expected value -1.Comment: RevTex4, 9 pages, 10 eps figures, Typos corrected. To be published in Phys. Rev. D(2004

Fragility of the A-type AF and CE Phases of Manganites: An Exotic Insulator-to-Metal Transition Induced by Quenched Disorder

Using Monte Carlo simulations and the two eg-orbital model for manganites, the stability of the CE and A-type antiferromagnetic insulating states is analyzed when quenched disorder in the superexchange JAF between the t2g localized spins and in the on-site energies is introduced. At vanishing or small values of the electron-(Jahn-Teller)phonon coupling, the previously hinted "fragility" of these insulating states is studied in detail, focusing on their charge transport properties. This fragility is here found to induce a rapid transition from the insulator to a (poor) metallic state upon the introduction of disorder. A possible qualitative explanation is presented based on the close proximity in energy of ferromagnetic metallic phases, and also on percolative ideas valid at large disorder strength. The scenario is compared with previously discussed insulator-to-metal transitions in other contexts. It is argued that the effect unveiled here has unique properties that may define a new class of giant effects in complex oxides. This particularly severe effect of disorder must be present in other materials as well, in cases involving phases that arise as a compromise between very different tendencies, as it occurs with striped states in the cuprates.Comment: 13 pages, 17 figures, RevTex 4, submitted for publicatio