Related papers: Three-dimensionalizing the eight-vertex model

We introduce the concept of bi-conformal transformation, as a generalization of conformal ones, by allowing two orthogonal parts of a manifold with metric $\G$ to be scaled by different conformal factors. In particular, we study their…

We construct all (2+1)-dimensional PDEs depending only on 2nd-order derivatives of unknown which have the Euler-Lagrange form and determine the corresponding Lagrangians. We convert these equations and their Lagrangians to two-component…

We show that if H is a hereditary finite dimensional algebra, M is a finitely generated H-module and B is a semisimple subalgebra of the endomorphism algebra of M, then the representation dimension of the corresponding triangular matrix…

Let $K$ denote a field and let $V$ denote a vector space over $K$ with finite positive dimension. We consider a pair of linear transformations $A:V\to V$ and $A^*:V\to V$ that satisfy both conditions below: (i) There exists a basis for $V$…

In the spirit of a previous study of the tetrahedral group $T \simeq A_4$, we discuss a minimalist scheme to derive the neutrino mixing matrix using the double tetrahedral group $T'$, the double cover of $T$. The new features are three…

We study the addditon problem for strongly matricially free random variables which generalize free random variables. Using operators of Toeplitz type, we derive a linearization formula for the `matricial R-transform' related to the…

Let $V$ denote a vector space over C with finite positive dimension. By a {\em Leonard triple} on $V$ we mean an ordered triple of linear operators on $V$ such that for each of these operators there exists a basis of $V$ with respect to…

We define an integrable lattice model which, in the notation of Yang, in addition to the conventional 2-particle $R$-matrices also contains non-reducible 3-particle $R$-matrices. The corresponding modified Yang-Baxter equations are solved…

We propose a notion of a ternary skew-symmetric covariant tensor of 3rd order, consider it as a 3-dimensional matrix and study a ten-dimensional complex space of these tensors. We split this space into a direct sum of two five-dimensional…

A parametrization of 3x3 unitary matrices is presented. This mathematical approach is inspired on polarization algebra and is formulated through the identification of a set of three orthonormal three-dimensional Jones vectors representing…

In three space dimensions, when a physical system possesses spherical symmetry, the dynamical equations automatically lead to the Legendre and the associated Legendre equations, with the respective orthogonal polynomials as their standard…

Kaluza-Klein reductions of 11-dimensional supergravity lead to exceptional global symmetries in lower dimensions. Certain non-geometric elements of these symmetries, parameterized by a tri-vector $\gamma$, are not inherited from the…

We propose an approach to construct three-dimensional lattice models using line defects in state integral models on shaped triangulations of 3-manifolds. The Boltzmann weights for these models satisfy a variant of the tetrahedron equation,…

Main goal of this paper is to generalize Hadamard's real part theorem and invariant forms of Borel-Carath\'eodory's theorem from complex analysis to solutions of the Riesz system in the three-dimensional Euclidean space in the framework of…

The diagonalisation of the transfer matrices of solvable vertex models with alternating spins is given. The crystal structure of (semi-)infinite tensor products of finite-dimensional $U_q(\hat{sl}_2)$ crystals with alternating dimensions is…

The eight-vertex model at the reflectionless points is considered on the basis of Smirnov's axiomatic approach. Integral formulae for form factors of the eight-vertex model can be obtained in terms of those of the eight-vertex SOS model, by…

We study the generalisation of Baxter's three-colour problem to a random lattice. Rephrasing the problem as a matrix model problem we discuss the analyticity structure and the critical behaviour of the resulting matrix model. Based on a set…

We give a characterization of all three points in $\mathbb R^4$ with integer coordinates which are at the same Euclidean distance apart. In three dimension the problem is characterized in terms of solutions of the Diophantine equations…

We generalize the three two-particle Bethe-Salpeter equations to ten three-particle ladders. These equations are exact and yield the exact three-particle vertex, if we knew the three-particle vertex irreducible in one of the ten channels.…

We model tri-bimaximal lepton mixing from first principles in a way that avoids the problem of the vacuum alignment characteristic of such models. This is achieved by using a softly broken A4 symmetry realized with an isotriplet fermion,…