XXZ Bethe states as highest weight vectors of the sl2sl_2 loop algebra at roots of unity

We show that every regular Bethe ansatz eigenvector of the XXZ spin chain at roots of unity is a highest weight vector of the $sl_2$ loop algebra, for some restricted sectors with respect to eigenvalues of the total spin operator $S^Z$, and evaluate explicitly the highest weight in terms of the Bethe roots. We also discuss whether a given regular Bethe state in the sectors generates an irreducible representation or not. In fact, we present such a regular Bethe state in the inhomogeneous case that generates a reducible Weyl module. Here, we call a solution of the Bethe ansatz equations which is given by a set of distinct and finite rapidities {\it regular Bethe roots}. We call a nonzero Bethe ansatz eigenvector with regular Bethe roots a {\it regular Bethe state}.Comment: 40pages; revised versio

Irreducibility criterion for a finite-dimensional highest weight representation of the sl(2) loop algebra and the dimensions of reducible representations

We present a necessary and sufficient condition for a finite-dimensional highest weight representation of the $sl_2$ loop algebra to be irreducible. In particular, for a highest weight representation with degenerate parameters of the highest weight, we can explicitly determine whether it is irreducible or not. We also present an algorithm for constructing finite-dimensional highest weight representations with a given highest weight. We give a conjecture that all the highest weight representations with the same highest weight can be constructed by the algorithm. For some examples we show the conjecture explicitly. The result should be useful in analyzing the spectra of integrable lattice models related to roots of unity representations of quantum groups, in particular, the spectral degeneracy of the XXZ spin chain at roots of unity associated with the $sl_2$ loop algebra.Comment: 32 pages with no figure; with corrections on the published versio

SiO Maser Survey of the Large-Amplitude Variables in the Galactic Center

We have surveyed ~400 known large-amplitude variables within 15' of the galactic center in the SiO J=1--0 v=1 and 2 maser lines at 43 GHz, resulting in 179 detections. SiO lines were also detected from 16 other resulting in 180 detections. SiO lines were also detected from 16 other sources, which are located within 20" (the telescope half beamwidth) of the program objects. The detection rate of 48 percent is comparable to that obtained in Bulge IRAS source surveys. Among the SiO detections, five stars have radial velocities greater than 200 km/s. The SiO detection rate increases steeply with the period of light variation, particularly for stars with P>500 d, where it exceeds 80%. We found that, at a given period, the SiO detection rate is approximately three times that for OH. These facts suggest that the large-amplitude variables in the Nuclear Disk region are AGB stars similar in their overall properties to the inner and outer Bulge IRAS/SiO sources. From the set of radial velocity data, the mass distribution within 30 pc of the galactic center is derived by a new method which is based on the collisionless Boltzmann equation integrated along the line of sight. The mass within 30 pc is about 6.4 [\pm 0.7] \times 10^7 M_{\odot} and the mass of the central black hole is 2.7 [\pm 1.3] \times 10^6 M_{\odot}. Consideration of the line-of-sight velocity of each star and its potential energy leads to the conclusion that the five high-velocity stars come from galactocentric distances as high as 300 pc. The high-velocity subsample of stars with negative radial velocities exhibits a tendency to have brighter K magnitudes than the subsample of stars with positive velocities. The origin of these high-velocity stars is discussed.Comment: Hires. figures are available as No.604 of NRO report at http://www.nro.nao.ac.jp/library/report/list.html . PASJ 56 (april 28 issue) in pres

SiO Maser Survey of IRAS Sources in the Inner Galactic Disk

We have surveyed 401 color selected IRAS sources in the Galactic disk in the SiO J=1--0 v= 1 and 2 maser lines at 43 GHz, resulting in 254 (239 new) detections. The observed sources lie mostly in a strip of the inner Galactic disk with boundaries -10<l<40 deg and |b|<3 deg. This survey provides radial velocities of inner-disk stars for which optical measurements cannot be made due to interstellar extinction. The SiO $l$--$v$ diagram in the area $-10<l<40 deg exhibits fewer objects coincident with the molecular ring feature than the OH 1612 MHz source$l$--$v$ map does, indicating a slight difference of stellar type between SiO and OH emitting stars. After identifying all of the SiO detected sources in the 2MASS near-infrared catalog, we computed their luminosity distances based on the infrared fluxes. We then mapped these objects onto the first quadrant of the Galactic plane. Combining the distances with the SiO radial-velocities, we obtained a pattern speed for SiO maser sources, Omega_P=21 (+- 13) km s^{-1} kpc^{-1}, between the distances 1 and 5.5 kpc, without the use of any dynamical models. The increase of the pattern speed toward the Galactic center (up to 60 km s^{-1} kpc^{-1} between the distances, 5.5 and 7 kpc) suggests the presence of two pattern speeds in the Galaxy.Comment: 38 page 9 figures, high res. eps files are available as NRO report No. 608 (http://www.nro.nao.ac.jp/library/report/list.html). PASJ 56 No. 4 in pres

Detections of SiO Masers from the Large-Amplitude Variables in the Galactic Nuclear Disk

We have surveyed known large-amplitude variables within 15' of the Galactic center in the SiO J=1-0 v=1 and 2 maser lines at 43 GHz, resulting in 79 detections and 58 non-detections. The detection rate of 58 percent is comparable to that obtained in Bulge IRAS source surveys. SiO lines were also detected from four other sources near the program objects. The SiO detection rate increases steeply with the period, particularly for stars with P>500 d, where it exceeds 80%. We found at a given period that the SiO detection rate is approximately double that for OH. These facts suggest that the large-amplitude variables in the Nuclear Disk region are AGB stars similar in their overall properties to the inner and outer bulge IRAS/SiO sources.Comment: 5 pages, 2 figures, 1 Table. PASJ 54, No 2 April 25 issue in pres

Multi-Colour Braid-Monoid Algebras

We define multi-colour generalizations of braid-monoid algebras and present explicit matrix representations which are related to two-dimensional exactly solvable lattice models of statistical mechanics. In particular, we show that the two-colour braid-monoid algebra describes the Yang-Baxter algebra of the critical dilute A-D-E models which were recently introduced by Warnaar, Nienhuis, and Seaton as well as by Roche. These and other solvable models related to dense and dilute loop models are discussed in detail and it is shown that the solvability is a direct consequence of the algebraic structure. It is conjectured that the Yang-Baxterization of general multi-colour braid-monoid algebras will lead to the construction of further solvable lattice models.Comment: 32 page

Dilute Birman--Wenzl--Murakami Algebra and Dn+1(2)D^{(2)}_{n+1} models

A ``dilute'' generalisation of the Birman--Wenzl--Murakami algebra is considered. It can be ``Baxterised'' to a solution of the Yang--Baxter algebra. The $D^{(2)}_{n+1}$ vertex models are examples of corresponding solvable lattice models and can be regarded as the dilute version of the $B^{(1)}_{n}$ vertex models.Comment: 11 page

Evolution of superconductivity by oxygen annealing in FeTe0.8S0.2

Oxygen annealing dramatically improved the superconducting properties of solid-state-reacted FeTe0.8S0.2, which showed only a broad onset of superconducting transition just after the synthesis. The zero resistivity appeared and reached 8.5 K by the oxygen annealing at 200\degree C. The superconducting volume fraction was also enhanced from 0 to almost 100%. The lattice constants were compressed by the oxygen annealing, indicating that the evolution of bulk superconductivity in FeTe0.8S0.2 was correlated to the shrinkage of lattice.Comment: 13 pages, 6 figure

Evolution of superconductivity in LaO1-xFxBiS2 prepared by high pressure technique

Novel BiS2-based superconductors LaO1-xFxBiS2 prepared by the high pressure synthesis technique were systematically studied. It was found that the high pressure annealing strongly the lattice as compared to the LaO1-xFxBiS2 samples prepared by conventional solid state reaction at ambient pressure. Bulk superconductivity was observed within a wide F-concentration range of x = 0.2 ~ 0.7. On the basis of those results, we have established a phase diagram of LaO1-xFxBiS2.Comment: 11 pages, 6 figure