相关论文: Three Blocks Solvable Lattice Models and Birman--M…

In this paper, we give the general forms of the minimal $L$ matrix (the elements of the $L$-matrix are $c$ numbers) associated with the Boltzmann weights of the $A_{n-1}^1$ interaction-round-a-face (IRF) model and the minimal representation…

We introduce triples of associative algebras as a tool for building solutions to the Yang-Baxter equation. It turns out that the class of R-matrices thus obtained is related to a Hecke-like condition, which is formulated for associative…

A representation of the Birman-Wenzl-Murakami algebra BW_{t}(-q^{2n},q) exists in the centraliser algebra End_{U_q(osp(1|2n))}(V^{\otimes t}), where V is the fundamental (2n+1)-dimensional irreducible U_{q}(osp(1|2n))-module. This…

The diagram algebra introduced by Brauer that describes the centralizer algebra on tensor products of the natural representation of an orthogonal group has a presentation by generators and relations that only depends on the graph of type An…

Matrix models and their connections to String Theory and noncommutative geometry are discussed. Various types of matrix models are reviewed. Most of interest are IKKT and BFSS models. They are introduced as 0+0 and 1+0 dimensional reduction…

We represent Feigin's construction [11] of lattice W algebras and give some simple results: lattice Virasoro and $W_3$ algebras. For simplest case $g=sl(2)$ we introduce whole $U_q(sl(2))$ quantum group on this lattice. We find simplest…

The Laplace-Beltrami problem on closed surfaces embedded in three dimensions arises in many areas of physics, including molecular dynamics (surface diffusion), electromagnetics (harmonic vector fields), and fluid dynamics (vesicle…

Let $G$ be a finite nonabelian group. We show how an endomorphism of $G$ with abelian image gives rise to a family of binary operations $\{\circ_n: n\in \mathbb Z^{\ge 0}\}$ on $G$ such that $(G,\circ_m,\circ_n)$ is a skew left brace for…

Supersymmetry algebras can be used to obtain algebraic expressions for constant Yang-Baxter solutions, also known as braid group generators. This was done for non-invertible braid operators in \cite{maity2025non}. In this work we extend…

The recent construction of integrable quantum field theories on two-dimensional Minkowski space by operator-algebraic methods is extended to models with a richer particle spectrum, including finitely many massive particle species…

We show that the Bagger-Lambert theory of multiple M2-branes fits into the general construction of maximally supersymmetric gauge theories using the embedding tensor technique. We apply the embedding tensor technique in order to…

A class of quasi two and three dimensional quantum lattice spin models with nearest and next nearest neighbour interactions is proposed. The basic idea of construction is to introduce interactions in an array of XXZ spin chains through…

Let X be a closed surface of genus two embedded in the 3-sphere. Then X inherits a metric and an orientation, which give an almost complex structure, which automatically integrates to a genuine complex structure, making X a Riemann surface.…

Components of the Moduli space of sheaves on a K3 surface are parametrized by a lattice; the (algebraic) Mukai lattice. Isometries of the Mukai lattice often lift to symplectic birational isomorphisms of the collection of components. An…

This article presents a study of an algebra spanned by the faces of a hyperplane arrangement. The quiver with relations of the algebra is computed and the algebra is shown to be a Koszul algebra. It is shown that the algebra depends only on…

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…

Intertwiners between \ade lattice models are presented and the general theory developed. The intertwiners are discussed at three levels: at the level of the adjacency matrices, at the level of the cell calculus intertwining the face…

The theory of correlated electron systems on a lattice proves notoriously complicated because of the exponential growth of Hilbert space. Mean-field approaches provide valuable insight when the self-energy has a dominant local structure.…

We give an explicit description of the vector bundle of WZW conformal blocks on elliptic curves with marked points as subbundle of a vector bundle of Weyl group invariant vector valued theta functions on a Cartan subalgebra. We give a…

We will study a linear first order system, a connection $\db$ problem, on a vector bundle equipped with a connection, over a Riemann surface. We show optimal conditions on the connection forms which allow one to find a holomorphic frame, or…