Related papers: The Many Faces of the Chiral Potts Model
Supersymmetry is studied in 2+1 dimensions. In addition to the multiplets corresponding to those in 3+1 dimensions the Clifford algebra allows an extra set. When the extra chiral multiplet is included, formulating supersymmetric QED3 in the…
This is a survey of recent developments in combinatorics. The goal is to give a big picture of its many interactions with other areas of mathematics, such as: group theory, representation theory, commutative algebra, geometry (including…
In this paper, we present the point symmetry group of three-dimensional homogeneous Helmholtz equation, when we consider the cylindrical coordinate system. In continuation, we present a complete set of functionally independent invariants of…
Isotopic pairs and their representations are considered in a general framework of the vector superalgebra. Numerous examples of finite-dimensional and infinite-dimensional isotopic pairs are discussed. Several types of their representations…
On the basis of empirical Fischer projections, we developed an algebraic approach to central molecular chirality of tetrahedral molecules. The elements of such an algebra are obtained from the 24 projections which a single chiral…
We propose a list of open problems in pluripotential theory partially motivated by their applications to complex differential geometry. The list includes both local questions as well as issues related to the compact complex manifold…
The appearance of quantum groups in conformal field theories is traced back to the Poisson-Lie symmetries of the classical chiral theory. A geometric quantization of the classical theory deforms the Poisson-Lie symmetries to the quantum…
We give an account of well known calculations of the RO(Q)-graded coefficient rings of some of the most basic Q-equivariant cohomology theories, where Q is a group of order 2. One purpose is to advertise the effectiveness of the Tate…
After mentioning some of the difficulties arising in lattice gauge theory from chiral symmetry, I discuss one of the recent attempts to resolve these issues using fermionic surface states in an extra space-time dimension. This picture can…
We explore the possibility of replacing point set topology by higher category theory and topos theory as the foundation for quantum general relativity. We discuss the BC model and problems of its interpretation, and connect with the…
We establish a hierarchy of quantum dilogarithm identities associated to a sequence of triangular shaped quivers. The tetrahedron equation plays a key role in our construction.
Chirality is of primary importance in many areas of chemistry and has been extensively investigated since its discovery. We introduce here the description of central chirality for tetrahedral molecules using a geometrical approach based on…
Motivated by representation theory and geometry, we introduce and develop an equivariant generalization of Ehrhart theory, the study of lattice points in dilations of lattice polytopes. We prove representation-theoretic analogues of…
Recent achievements in the heavy quark theory are critically reviewed. The emphasis is put on those aspects which either did not attract enough attention or cause heated debates in the current literature. Among other topics we discuss (i)…
This article surveys modularity, level raising and level lowering questions for two-dimensional representations modulo prime powers of the absolute Galois group of the rational numbers. It contributes some new results and describes…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
An introduction to the basic ideas and methods of Chiral Perturbation Theory is presented. Several phenomenological applications of the effective Lagrangian technique to strong, electromagnetic and weak interactions are discussed.
This paper deals with the evaluation of some definite Euler-type integrals in terms of the Wright hypergeometric function. We obtain a theorem on the Wright hypergeometric function and then use this theorem to evaluate some definite…
We derive the order parameter of the chiral Potts model, using the method of Jimbo et al. The result agrees with previous conjectures.
In this work, families of kinks are analytically identified in multifield theories with either polynomial or deformed sine-Gordon-type potentials. The underlying procedure not only allows us to obtain analytical solutions for these models,…