3,932 research outputs found

### Elliptic Quantum Group U_{q,p}(\hat{sl}_2) and Vertex Operators

Introducing an H-Hopf algebroid structure into U_{q,p}(\widedhat{sl}_2), we
investigate the vertex operators of the elliptic quantum group
U_{q,p}(\widedhat{sl}_2) defined as intertwining operators of infinite
dimensional U_{q,p}(\widedhat{sl}_2)-modules. We show that the vertex operators
coincide with the previous results obtained indirectly by using the quasi-Hopf
algebra B_{q,\lambda}(\hat{sl}_2). This shows a consistency of our H-Hopf
algebroid structure even in the case with non-zero central element.Comment: 15 pages. Typos fixed. Version to appear in J.Phys.A :Math.and
Theor., special issue on Recent Developments in Infinite Dimensional Algebras
and Their Applications to Quantum Integrable Systems 200

### Relativistic models of magnetars: Nonperturbative analytical approach

In the present paper we focus on building simple nonperturbative analytical
relativistic models of magnetars. With this purpose in mind we first develop a
method for generating exact interior solutions to the static and axisymmetric
Einstein-Maxwell-hydrodynamic equations with anisotropic perfect fluid and with
pure poloidal magnetic field. Then using an explicit exact solution we present
a simple magnetar model and calculate some physically interesting quantities as
the surface elipticity and the total energy of the magnetized star.Comment: 10 pages, LaTe

### Elliptic algebra U_{q,p}(^sl_2): Drinfeld currents and vertex operators

We investigate the structure of the elliptic algebra U_{q,p}(^sl_2)
introduced earlier by one of the authors. Our construction is based on a new
set of generating series in the quantum affine algebra U_q(^sl_2), which are
elliptic analogs of the Drinfeld currents. They enable us to identify
U_{q,p}(^sl_2) with the tensor product of U_q(^sl_2) and a Heisenberg algebra
generated by P,Q with [Q,P]=1. In terms of these currents, we construct an L
operator satisfying the dynamical RLL relation in the presence of the central
element c. The vertex operators of Lukyanov and Pugai arise as `intertwiners'
of U_{q,p}(^sl_2) for level one representation, in the sense to be elaborated
on in the text. We also present vertex operators with higher level/spin in the
free field representation.Comment: 49 pages, (AMS-)LaTeX ; added an explanation of integration contours;
added comments. To appear in Comm. Math. Phys. Numbering of equations is
correcte

### Maximization of a Convex Quadratic Function Under Linear Constraints

This paper addresses the maximization of a convex quadratic function subject to linear constraints. We first prove the equivalence of this problem to the associated bilinear program. Next we apply a theory of bilinear programming to compute a local maximum and to generate a cutting plane which eliminates a region containing that local maximum. Then we develop an iterative procedure to improve a given cut by exploiting the symmetric structure of the bilinear program. This procedure either generates a point which is strictly better than the best local maximum found, or generates a cut which is deeper (usually much deeper) than Tui's cut. Finally the results of numerical experiments on small problems are reported

### A Cutting Plane Algorithm for Solving Bilinear Programs

Nonconvex programs which have either a nonconvex minimand and/or a nonconvex feasible region have been considered by most mathematical programmers as a hopelessly difficult area of research. There are, however, two exceptions where considerable effort to obtain a global optimum is under way. One is integer linear programming and the other is nonconvex quadratic programming. This paper addresses itself to a special class of nonconvex quadratic program referred to as a "bilinear program" in the literature. We will propose here a cutting plane algorithm to solve this class of problems

### Maximization of a Convex Quadratic Function Under Linear Constraints

Since the appearance of a paper by H. Tui, maximization of convex function over a polytope has attracted much attention. In his paper, two algorithms were proposed: one cutting plane and the other enumerative. However, the numerical experiments reported on the naive cutting plane approach were discouraging enough to shift the researchers more to the direction of enumerative approaches.
In this paper, we will develop a cutting plane algorithm for maximizing a convex quadratic function subject to linear constraints. The basic idea is much the same as Tui's method. It also parallels some of the recent results by E. Balas and C-A. Burdet. We will, however, use standard tools which are easier to understand and will fully exploit the special structure of the problem. The main purpose of the paper is to demonstrate that the full exploitation of special structure will enable us to generate a cut which is much deeper than Tui's cut and that the cutting plane algorithm can be used to solve a rather big problem efficiently

### The Vertex-Face Correspondence and the Elliptic 6j-symbols

A new formula connecting the elliptic $6j$-symbols and the fusion of the
vertex-face intertwining vectors is given. This is based on the identification
of the $k$ fusion intertwining vectors with the change of base matrix elements
from Sklyanin's standard base to Rosengren's natural base in the space of even
theta functions of order $2k$. The new formula allows us to derive various
properties of the elliptic $6j$-symbols, such as the addition formula, the
biorthogonality property, the fusion formula and the Yang-Baxter relation. We
also discuss a connection with the Sklyanin algebra based on the factorised
formula for the $L$-operator.Comment: 23 page

### Free Field Approach to the Dilute A_L Models

We construct a free field realization of vertex operators of the dilute A_L
models along with the Felder complex. For L=3, we also study an E_8 structure
in terms of the deformed Virasoro currents.Comment: (AMS-)LaTeX(2e), 43page

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