Free field approach to diagonalization of boundary transfer matrix : recent advances

We diagonalize infinitely many commuting operators $T_B(z)$. We call these operators $T_B(z)$ the boundary transfer matrix associated with the quantum group and the elliptic quantum group. The boundary transfer matrix is related to the solvable model with a boundary. When we diagonalize the boundary transfer matrix, we can calculate the correlation functions for the solvable model with a boundary. We review the free field approach to diagonalization of the boundary transfer matrix $T_B(z)$ associated with $U_q(A_2^{(2)})$ and $U_{q,p}(\hat{sl_N})$. We construct the free field realizations of the eigenvectors of the boundary transfer matrix $T_B(z)$. This paper includes new unpublished formula of the eigenvector for $U_q(A_2^{(2)})$. It is thought that this diagonalization method can be extended to more general quantum group $U_q(g)$ and elliptic quantum group $U_{q,p}(g)$.Comment: To appear in Group 28 : Group Theoretical Method in Physic

The Interpretation of Near-Infrared Star Counts at the South Galactic Pole

We present new deep $K'$ counts of stars at the South Galactic Pole (SGP) taken with the NAOJ PICNIC camera to $K'=17.25$. Star-galaxy separation to $K'=17.5$ was accomplished effectively using image profiles because the pixel size we used is 0.509 arcsec. We interpret these counts using the SKY (Cohen 1994) model of the Galactic point source sky and determine the relative normalization of halo-to-disk populations, and the location of the Sun relative to the Galactic plane, within the context of this model. The observed star counts constrain these parameters to be: halo/disk $\sim$ 1/900 and z$_\odot$=16.5$\pm$2.5 pc. These values have been used to correct our SGP galaxy counts for contamination by the point source Galactic foreground.Comment: accepted for publication in AJ, 15 pages with 2 figure

Big-Bang Nucleosynthesis with Unstable Gravitino and Upper Bound on the Reheating Temperature

We study the effects of the unstable gravitino on the big-bang nucleosynthesis. If the gravitino mass is smaller than \sim 10 TeV, primordial gravitinos produced after the inflation are likely to decay after the big-bang nucleosynthesis starts, and the light element abundances may be significantly affected by the hadro- and photo-dissociation processes as well as by the p n conversion process. We calculate the light element abundances and derived upper bound on the reheating temperature after the inflation. In our analysis, we calculate the decay parameters of the gravitino (i.e., lifetime and branching ratios) in detail. In addition, we performed a systematic study of the hadron spectrum produced by the gravitino decay, taking account of all the hadrons produced by the decay products of the gravitino (including the daughter superparticles). We discuss the model-dependence of the upper bound on the reheating temperature.Comment: 32 pages, 11 figure

The Infrared Cloud Monitor for the MAGNUM Robotic Telescope at Haleakala

We present the most successful infrared cloud monitor for a robotic telescope. This system was originally developed for the MAGNUM 2-m telescope, which has been achieving unmanned and automated monitoring observation of active galactic nuclei at Haleakala on the Hawaiian island of Maui since 2001. Using a thermal imager and two aspherical mirrors, it at once sees almost the whole sky at a wavelength of $\lambda\sim 10\mu{\rm m}$. Its outdoor part is weather-proof and is totally maintenance-free. The images obtained every one or two minutes are analysed immediately into several ranks of weather condition, from which our automated observing system not only decides to open or close the dome, but also selects what types of observations should be done. The whole-sky data accumulated over four years show that 50$-$60 % of all nights are photometric, and about 75 % are observable with respect to cloud condition at Haleakala. Many copies of this system are now used all over the world such as Mauna Kea in Hawaii, Atacama in Chile, and Okayama and Kiso in Japan.Comment: 18 pages, 15 figures, 7 tables, accepted for publication in PAS

Electronic structure and effects of dynamical electron correlation in ferromagnetic bcc-Fe, fcc-Ni and antiferromagnetic NiO

LDA+DMFT method in the framework of the iterative perturbation theory (IPT) with full LDA Hamiltonian without mapping onto the effective Wannier orbitals. We then apply this LDA+DMFT method to ferromagnetic bcc-Fe and fcc-Ni as a test of transition metal, and to antiferromagnetic NiO as an example of transition metal oxide. In Fe and Ni, the width of occupied 3d bands is narrower than those in LDA and Ni 6eV satellite appears. In NiO, the resultant electronic structure is of charge-transfer insulator type and the band gap is 4.3eV. These results are in good agreement with the experimental XPS. The configuration mixing and dynamical correlation effects play a crucial role in these results

Elliptic Deformed Superalgebra uq,p(sl^(M∣N))u_{q,p}(\hat{{sl}}(M|N))

We introduce the elliptic superalgebra $U_{q,p}(\hat{sl}(M|N))$ as one parameter deformation of the quantum superalgebra $U_q(\hat{sl}(M|N))$. For an arbitrary level $k \neq 1$ we give the bosonization of the elliptic superalgebra $U_{q,p}(\hat{sl}(1|2))$ and the screening currents that commute with $U_{q,p}(\hat{sl}(1|2))$ modulo total difference.Comment: LaTEX, 25 page

The Elliptic Algebra U_{q,p}(sl_N^) and the Deformation of W_N Algebra

After reviewing the recent results on the Drinfeld realization of the face type elliptic quantum group B_{q,lambda}(sl_N^) by the elliptic algebra U_{q,p}(sl_N^), we investigate a fusion of the vertex operators of U_{q,p}(sl_N^). The basic generating functions \Lambda_j(z) (j=1,2,.. N-1) of the deformed W_N algebra are derived explicitly.Comment: 15 pages, to appear in Journal of physics A special issue - RAQIS0

The Integrals of Motion for the Deformed W-Algebra Wqt(slN)W_{qt}(sl_N^) II: Proof of the commutation relations

We explicitly construct two classes of infinitly many commutative operators in terms of the deformed W-algebra $W_{qt}(sl_N^)$, and give proofs of the commutation relations of these operators. We call one of them local integrals of motion and the other nonlocal one, since they can be regarded as elliptic deformation of local and nonlocal integrals of motion for the $W_N$ algebra.Comment: Dedicated to Professor Tetsuji Miwa on the occasion on the 60th birthda