Quasi-Hopf twistors for elliptic quantum groups

The Yang-Baxter equation admits two classes of elliptic solutions, the vertex type and the face type. On the basis of these solutions, two types of elliptic quantum groups have been introduced (Foda et al. [FIJKMY1], Felder [Fe]). Frønsdal [Fr1, Fr2] made a penetrating observation that both of them are quasi-Hopf algebras, obtained by twisting the standard quantum affine algebraU _q(g). In this paper we present an explicit formula for the twistors in the form of an infinite product of the universalR matrix ofU _q(g). We also prove the shifted cocycle condition for the twistors, thereby completing Frønsdal's findings.This construction entails that, for generic values of the deformation parameters, the representation theory forU _q(g) carries over to the elliptic algebras, including such objects as evaluation modules, highest weight modules and vertex operators. In particular, we confirm the conjectures of Foda et al. concerning the elliptic algebraA _q,p ( ).Dedicated to Professor Mikio Sato on the occasion of his seventieth birthday     

Adsorption of tetramethylthiourea at the mercury/water interface

The adsorption of tetramethylthiourea was studied by means of differential capacity measurements. Various parameters have been obtained by back-integration. The extent of orientation of the organic molecule has been estimated from the experimental adsorption potential shift by subtracting the contribution due to adsorbed water molecules calculated according to the Bockris-Habib model. Adsorption of tetramethylthiourea has been found to obey a Frumkin isotherm with the interaction parameter depending on the electric field. A scenario is proposed where different possible orientations are suggested, depending on charge sign and coverage. Such a change in orientation has been interpreted in terms of the electronic polarization effect.     

Intersection Numbers of Twisted Cycles Associated with the Selberg Integral and an Application to the Conformal Field Theory

Intersection numbers of twisted (or loaded) cycles associated with the Selberg integral are studied. In particular, the self-intersection number of the cycle which is invariant under the action of the symmetric group is expressed by the product of trigonometric functions. This formula reproduces the four-point correlation functions in the conformal field theory calculated by Dotsenko-Fateev in [3]. In our study, a compact non-singular model (Terada model) of the configuration space of n+3 points on the real projective line and a q-analogue of the Chu-Vadermonde formula for the hypergeometric series play a crucial role. Intersection numbers of the corresponding cocycles are also studied.This is a revised version of Intersection numbers of twisted cycles and the correlation functions of the conformal field theory, Kyushu Univ. preprint series 2002-23.     

Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent

The quantal system of Bose particles described by the non-linear Schrödinger equation i?φ/?t = -$\text{1}\text{2}$?²φ/?x² + cφ1φ², with c= cxf∞ and via the ground state with finite particle density, is the 1- dimensional gas of impenetrable bosons studied by M. Girardeau, T.D. Schultz, A. Lenard, H.G. Vaidya and C.A. Tracy. We show that the 2-point (resp. 2n-point) function, or the 1-particle (resp. n-particle) reduced density matrix, of this system satisfies a non-linear differential equation (resp. a system of non-linear partial differential equations) of Painlevé type. Derivation of these equations is based on the link between field operators in a Clifford group and monodromy preserving deformation theory, which was previously established and applied to the 2-dimensional Ising model and other problems. Several related topics are also discussed.     

On 1-rotational Sλ(2, 3, ν) designs

In this paper, the necessary and sufficient condition for the existence of a 1-rotational S_λ (2, 3, ν) design is obtained, and it is shown that an S_λ (2, 3, ν) design, if it exists, can be always constructed cyclically.     

Some remarks on the differential approach to the star-triangle relation

Some working hypotheses are proposed to solve the star-triangle relation by the differential method. They are applied to and checked by three-and four-state IRF model with a symmetry condition. Several solutions involving elliptic or trigonometric functions are presented.     

Jackson’s integral of the Hurwitz zeta function

We give a Jacksonq-integral analogue of Euler’s logarithmic sine integral established in 1769 from several points of view, specifically from the one relating to the Hurwitz zeta function. Partially supported by Grant-in-Aid for Exploratory Research No. 15654003. Partially supported by Grant-in-Aid for Scientific Research (B) No. 15340003. Partially supported by Grant-in-Aid for Scientific Research (B) No. 15340012.     

Field-reversed configuration maintained by rotating magnetic field with high spatial harmonics

Field-reversed configurations (FRCs) driven by rotating magnetic fields (RMFs) with spatial high harmonics have been studied in the metal flux conserver of the FRC injection experiment. The experimental results show that the fundamental RMF component is observed to penetrate the plasma column, while the high harmonics are screened at the plasma edge due to their slower or reversed rotation. This selective penetration of the RMF provides good compatibility of radial and azimuthal force balances; significant radial inward force mostly from the high-harmonic components, and sufficient azimuthal torque solely provided by the fundamental component.     

Hidden Grassmann Structure in the XXZ Model

For the critical XXZ model, we consider the space of operators which are products of local operators with a disorder operator. We introduce two anti-commutative families of operators which act on . These operators are constructed as traces over representations of the q-oscillator algebra, in close analogy with Baxter’s Q-operators. We show that the vacuum expectation values of operators in can be expressed in terms of an exponential of a quadratic form of . On leave of absence from Skobeltsyn Institute of Nuclear Physics, MSU, 119992, Moscow, Russia Membre du CNRS