The decomposition of level-1 irreducible highest weight modules with respect to the level-0 actions of the quantum affine algebra Uq′(sl^n)U'_q(\hat{sl}_n)

We decompose the level-1 irreducible highest weight modules of the quantum affine algebra $U_q(\hat{sl}_n)$ with respect to the level-0 $U'_q (\hat{sl}_n)$--action defined in q-alg/9702024. The decomposition is parameterized by the skew Young diagrams of the border strip type.Comment: 22 pages, AMSLaTe

Out-of-plane dielectric constant and insulator-superconductor transition in Bi_2Sr_2Dy_{1-x}Er_xCu_2O_8 single crystals

The out-of-plane dielectric constant of the parent insulator of the high-temperature superconductor Bi_2Sr_2(Dy,Er)Cu_2O_8 was measured and analysed from 80 to 300 K in the frequency range of 10^6-10^9 Hz. All the samples were found to show a fairly large value of 10-60, implying some kind of charge inhomogeneity in the CuO_2 plane. Considering that the superconducting sample Bi_2Sr_2(Ca,Pr)Cu_2O_8 also shows a similar dielectric constant, the charge inhomogeneity plays an important role in the insulator-superconductor transition.Comment: RevTex4 format, 5 pages, 3 figures, submitted to J. Phys. Condens. Ma

Particle Propagator of Spin Calogero-Sutherland Model

Explicit-exact expressions for the particle propagator of the spin 1/2 Calogero-Sutherland model are derived for the system of a finite number of particles and for that in the thermodynamic limit. Derivation of the expression in the thermodynamic limit is also presented in detail. Combining this result with the hole propagator obtained in earlier studies, we calculate the spectral function of the single particle Green's function in the full range of the energy and momentum space. The resultant spectral function exhibits power-law singularity characteristic to correlated particle systems in one dimension.Comment: 43 pages, 6 figure

Exact spin dynamics of the 1/r^2 supersymmetric t-J model in a magnetic field

The dynamical spin structure factor S^{zz}(Q,omega) in the small momentum region is derived analytically for the one-dimensional supersymmetric t-J model with 1/r^2 interaction. Strong spin-charge separation is found in the spin dynamics. The structure factor S^{zz}(Q,omega) with a given spin polarization does not depend on the electron density in the small momentum region. In the thermodynamic limit, only two spinons and one antispinon (magnon) contribute to S^{zz}(Q,omega). These results are derived via solution of the SU(2,1) Sutherland model in the strong coupling limit.Comment: 20 pages, 8 figures. Accepted for publication in J.Phys.

Quantum affine Gelfand-Tsetlin bases and quantum toroidal algebra via K-theory of affine Laumon spaces

Laumon moduli spaces are certain smooth closures of the moduli spaces of maps from the projective line to the flag variety of GL_n. We construct the action of the quantum loop algebra U_v(Lsl_n) in the equivariant K-theory of Laumon spaces by certain natural correspondences. Also we construct the action of the quantum toroidal algebra U^{tor}_v(Lsl}_n) in the equivariant K-theory of the affine version of Laumon spaces. We write down explicit formulae for this action in the affine Gelfand-Tsetlin base, corresponding to the fixed point base in the localized equivariant K-theory.Comment: v2: multiple typos fixed, proofs of Theorems 4.13 and 4.19 expanded, 23 pages. v3: formulas of Theorems 4.9 and 4.13 corrected, resulting minor changes added. arXiv admin note: text overlap with arXiv:0812.4656, arXiv:math/0503456, arXiv:0806.0072 by other author

Rodrigues Formula for the Nonsymmetric Multivariable Hermite Polynomial

Applying a method developed by Takamura and Takano for the nonsymmetric Jack polynomial, we present the Rodrigues formula for the nonsymmetric multivariable Hermite polynomial.Comment: 5 pages, LaTe

Transport Properties of Bi2_2Sr2−x_{2-x}Lax_xCaCu2_2O8+δ_{8+\delta} Single Crystals Grown by a Floating-Zone Method

A parent insulator of the Bi-based high-$T_c$ superconductor Bi$_2$Sr$_{2-x}$La$_x$CaCu$_2$O$_{8+\delta}$ was successfully grown by a traveling solvent floating zone method. The in-plane resistivity $\rho_{ab}$ shows metallic behavior ($d\rho_{ab}/dT >$ 0) near room temperature, although the magnitude of the resistivity is far above the Mott limit for metallic conduction. The Hall mobility of the parent insulator does not so much differ from that of an optimally doped sample. These results suggest that the system is not a simple insulator with a well-defined gap, and the hole in the parent insulator is essentially itinerant, as soon as it is doped.Comment: 4pages, 4 figures, proceedings of International Symposium on Superconductivity 2002, Physica

On polynomial solutions of Heun equation

By making use of a recently developed method to solve linear differential equations of arbitrary order, we find a wide class of polynomial solutions to the Heun equation. We construct the series solution to the Heun equation before identifying the polynomial solutions. The Heun equation extended by the addition of a term, - \s/x, is also amenable for polynomial solutions.Comment: 4 pages, No figur