Related papers: The modified tetrahedron equation and its solution…
Here we demonstrate that the sixth order (in derivatives) spin-3 self-dual model can be obtained from the fifth order self-dual model via a Noether Gauge Embedding (NGE) of longitudinal Weyl transformations…
A new integrable model which is a variant of the one-dimensional Hubbard model is proposed. The integrability of the model is verified by presenting the associated quantum R-matrix which satisfies the Yang-Baxter equation. We argue that the…
The multiplicative multiple Horn problem is asking to determine possible singular values of the combinations $AB, BC$ and $ABC$ for a triple of invertible matrices $A,B,C$ with given singular values. There are similar problems for…
Let M be an oriented compact 3-manifold and let T be a (loose) triangulation of M, with ideal vertices at the components of the boundary of M and possibly internal vertices. We show that any spin structure s on M can be encoded by extra…
This paper continues the series begun with works solv-int/9701016 and solv-int/9702004. Here we show how to construct eigenstates for a model based on tetrahedron equation using the tetrahedral Zamolodchikov algebras. This yields, in…
The three-manifold topological invariants $\hat Z$ capture the half-index of the three-dimensional theory with ${\mathcal{N}}=2$ supersymmetry obtained by compactifying the M5 brane theory on the closed three-manifold. In 2019, surprising…
Position operator $\hat{r}$ appears as $i{\partial_p}$ in wave mechanics, while its matrix form is well known diverging in diagonals, causing serious difficulties in basis transformation, observable yielding, etc. We aim to find a…
The W_3 algebra of central charge 6/5 is realized as a subalgebra of the vertex operator algebra V_{\sqrt{2}A_2} associated with a lattice of type \sqrt{2}A_2 by using both coset construction and orbifold theory. It is proved that W_3 is…
We discuss what has been achieved in the past twenty years on the construction and study of a braided finite tensor category structure on a suitable module category for a suitable vertex operator algebra. We identify the main difficult…
We present a technique for producing valid dual bounds for nonconvex quadratic optimization problems. The approach leverages an elegant piecewise linear approximation for univariate quadratic functions due to Yarotsky, formulating this…
We introduce a homothetic extension of classical Weyl integrable geometry by generalizing the usual linear gauge transformations to affine homothetic transformations centered at a distinguished harmonic, scale-invariant form $\alpha_d$.…
The notion of the genus of a quadratic form is generalized to vertex operator algebras. We define it as the modular braided tensor category associated to a suitable vertex operator algebra together with the central charge. Statements…
We describe how to implement the conformal bootstrap program in the context of the embedding space OPE formalism introduced in previous work. To take maximal advantage of the known properties of the scalar conformal blocks for…
We describe a new Maple package for treating boundary problems for linear ordinary differential equations, allowing two-/multipoint as well as Stieltjes boundary conditions. For expressing differential operators, boundary conditions, and…
We construct a solution to pentagon equation with anticommuting variables living on two-dimensional faces of tetrahedra. In this solution, matrix coordinates are ascribed to tetrahedron vertices. As matrix multiplication is noncommutative,…
We propose to take a look at a new approach to the study of integral polyhedra. The main idea is to give an integral representation, or matrix model representation, for the key combinatorial characteristics of integral polytopes. Based on…
We construct a new solution to the tetrahedron equation by further pursuing the quantum cluster algebra approach in our previous works. The key ingredients include a symmetric butterfly quiver attached to the wiring diagrams for the longest…
Aircraft models may be considered as flat if one neglects some terms associated to aerodynamics. Computational experiments in Maple show that in some cases a suitably designed feed-back allows to follow such trajectories, when applied to…
We study solutions of a quadratic matrix equation arising in Riemannian geometry. Let $S$ be a real symmetric $n\times n$-matrix with zeros on the diagonal and let $\theta$ be a real number. We construct nonzero solutions $(S,\theta)$ of…
We review recent progress towards the solution of exactly solved isotropic vertex models with arbitrary toroidal boundary conditions. Quantum space transformations make it possible the diagonalization of the corresponding transfer matrices…