Intertwining Operators for a Degenerate Double Affine Hecke Algebra and Multivariable Orthogonal Polynomials

Operators that intertwine representations of a degenerate version of the double affine Hecke algebra are introduced. Each of the representations is related to multi-variable orthogonal polynomials associated with Calogero-Sutherland type models. As applications, raising operators and shift operators for such polynomials are constructed.Comment: 26 pages, LaTeX using epsf.sty, one figur

A study on the conversion of carotene into vitamin A by fluorescence microphotometry

For the purpose to confirm whether carotene is converted into vitamin A mainly in the intestine, fluorescence microscope observations as well as the fluorescence microphotometry for the estimation of fading state of the fluorescence were carried out on the fresh sections of the intestine, lung and liver of rats after oral administration of 11-carotene dissolved in oil, and suspended in water, and vitamin A in sesame oil as control. Yellowsih-green fluorescence of carotene is similar to that of vitamin A in color but the fluorescence of vitamin A fades away very rapidly within one minute while that of carotene does not fade or fade more slowly than that of vitamin A. Observations have revealed that, contrary to expectation, the administered carotene is not so readily converted into vitamin A in the intestinal mucosa, but after passing through the intestine without conversion to vitamin A, it is transported to the mesenteric lymph vessels, portal vein, and reaches the liver. In the liver, carotene appears as fatty droplets or micronized particles in the parenchymal cell. The conversion of carotene into vitamin A could not be observed in the intestine, liver and lung in the observations made one hour after the oral adminstration of carotene. Hower, it seems that carotene dissolved in minute fat droplets may be converted into vitamin A at water phase in tissues, after dissolution of carotene in fat and micronization of the fat droplets.</p

Anomalous diffusion analysis of the lifting events in the event-chain Monte Carlo for the classical XY models

We introduce a novel random walk model that emerges in the event-chain Monte Carlo (ECMC) of spin systems. In the ECMC, the lifting variable specifying the spin to be updated changes its value to one of its interacting neighbor spins. This movement can be regarded as a random walk in a random environment with a feedback. We investigate this random walk numerically in the case of the classical XY model in 1,2, and 3 dimensions to find that it is superdiffusive near the critical point of the underlying spin system. It is suggested that the performance improvement of the ECMC is related to this anomalous behavior.Comment: 7 pages, 5 figures. (v2) Presentation including plots reorganized. Discussion of exponents in the infinite system size limit adde

On three-dimensional topological field theories constructed from Dω(G)D^\omega(G) for finite group

We investigate the 3d lattice topological field theories defined by Chung, Fukuma and Shapere. We concentrate on the model defined by taking a deformation \D{G} of the quantum double of a finite commutative group $G$ as the underlying Hopf algebra. It is suggested that Chung-Fukuma-Shapere partition function is related to that of Dijkgraaf-Witten by \zcfs = |\zdw|^2 when $G=\Z_{2N+1}$. For $G=\Z_{2N}$, such a relation does not hold.Comment: 13 pages, 3 PS figures include