相关论文: Logarithmic Minimal Models

Exact results for conformational statistics of compact polymers are derived from the two-flavour fully packed loop model on the square lattice. This loop model exhibits a two-dimensional manifold of critical fixed points each one…

For logarithmically divergent one-loop lattice Feynman integrals I(p,a), subject to mild general conditions, we prove the following expected and crucial structural result: I(p,a) = f(p)log(aM)+g(p)+h(p,M) up to terms which vanish for…

Extended affine root systems appear as the root systems of extended affine Lie algebras. A subclass of extended affine root systems, whose elements are called ``minimal" turns out to be of special interest mostly because of the geometric…

We describe a novel Yang-Baxter integrable vertex model. From this vertex model we construct a certain class of partition functions that we show are equal to the LLT polynomials of Lascoux, Leclerc, and Thibon. Using the vertex model…

We study a quantum Yang-Baxter structure associated with non-ultralocal lattice models. We discuss the canonical structure of a class of integrable quantum mappings, i.e. canonical transformations preserving the basic commutation relations.…

The basic properties of the Temperley-Lieb algebra $TL_n$ with parameter $\beta = q + q^{-1}$, for $q$ any non-zero complex number, are reviewed in a pedagogical way. The link and standard (cell) modules that appear in numerous physical…

In this paper we consider the structure and representation theory of truncated current algebras $\mathfrak{g}_m = \mathfrak{g}[t]/(t^{m+1})$ associated to the Lie algebra $\mathfrak{g}$ of a standard reductive group over a field of positive…

This work concerns the boundary integrability of the ${\cal{U}}_{q}[osp(1|2)]$ Temperley-Lieb model. We constructed the solutions of the graded reflection equations in order to determine the boundary terms of the correspondig spin-1…

We find the fusion rules for the c_{p,1} series of logarithmic conformal field theories. This completes our attempts to generalize the concept of rationality for conformal field theories to the logarithmic case. A novelty is the appearance…

In this paper and its sequel, we construct topologically invariant defects in two-dimensional classical lattice models and quantum spin chains. We show how defect lines commute with the transfer matrix/Hamiltonian when they obey the defect…

In the spirit of Klein's Erlangen Program, we investigate the geometric and algebraic structure of fundamental line complexes and the underlying privileged discrete integrable system for the minors of a matrix which constitute associated…

We construct colored lattice models whose partition functions represent symplectic and odd orthogonal Demazure characters and atoms. We show that our lattice models are not solvable, but we are able to show the existence of sufficiently…

To provide tools, especially L-operators, for use in studies of rational Yang-Baxter algebras and quantum integrable models when the Lie algebras so(N) (b_n, d_n) or sp(2n) (c_n) are the invariance algebras of their R matrices, this paper…

Unitary representations of the Temperley-Lieb algebra $TL_N(Q)$ on the tensor space $({\mathbb C^n})^{\otimes N}$ are considered. Two criteria are given for determining when an orthogonal projection matrix $P$ of a rank $r$ gives rise to…

A space of local martingales of SLE type growth processes forms a representation of Virasoro algebra, but apart from a few simplest cases not much is known about this representation. The purpose of this article is to exhibit examples of…

Our goal is to develop a more general scheme for constructing integrable lattice regularisations of integrable quantum field theories. Considering the affine Toda theories as examples, we show how to construct such lattice regularisations…

We study properties of Hamiltonian integrable systems with random initial data by considering their Lax representation. Specifically, we investigate the spectral behaviour of the corresponding Lax matrices when the number $N$ of degrees of…

Let $\mathcal{O}_c$ be the category of finite-length modules for the Virasoro Lie algebra at central charge $c$ whose composition factors are irreducible quotients of reducible Verma modules. For any $c\in\mathbb{C}$, this category admits…

I choose the Lee-Yang model and go through different approaches to analyze it using the form factor approach and the bootstrap program, the lattice description and the lattice TBA equations for a full understanding of the model. The…

Let $p$ be a prime. We study the structure of and the inclusion relations among the terms in the monomial lattice in the modular symmetric power representations of $\mathrm{GL}_2(\mathbb{F}_p)$. We also determine the structure of certain…