Related papers: Combinatorial aspects of boundary loop models
Recent computational investigations in polymeric and non-polymeric binary mixtures have reported anomalous relaxation features when both components exhibit very different mobilities. Anomalous relaxation is characterized by sublinear power…
This paper is the first in a series where we attempt to define defects in critical lattice models that give rise to conformal field theory topological defects in the continuum limit. We focus mostly on models based on the Temperley-Lieb…
We consider a two matrix model with gaussian interaction involving the term $tr ABAB$, which is quartic in angular variables. It describes a vertex model (in particular case - of F-model type) on the lattice of fluctuating geometry and is…
We study properties of the category of modules of an algebra object A in a tensor category C. We show that the module category inherits various structures from C, provided that A is a Frobenius algebra with certain additional properties. As…
We continue our investigation of the two-dimensional Abelian sandpile model in terms of a logarithmic conformal field theory with central charge c=-2, by introducing two new boundary conditions. These have two unusual features: they carry…
Some combinatorial properties of fixed boundary rhombus random tilings with octagonal symmetry are studied. A geometrical analysis of their configuration space is given as well as a description in terms of discrete dynamical systems, thus…
In critical loop models, we define diagonal boundaries as boundaries that couple to diagonal fields only. Using analytic bootstrap methods, we show that diagonal boundaries are characterised by one complex parameter, analogous to the…
We consider a higher gauge topological model in three spatial dimensions whose input datum is a 2-group encoding the mixing of a 0-form $\mathbb Z_2$- and 1-form $\mathbb Z_3$-symmetry. We study the excitation content of the theory on the…
Using approximations, we give several characterizations of separability of bimodules. We also discuss how separability properties can be used to transfer some representation theoretic properties from one ring to another one: contravariant…
Various structural properties of the space of symmetry breaking boundary conditions that preserve an orbifold subalgebra are established. To each such boundary condition we associate its automorphism type. It is shown that correlation…
Arithmetic combinatorics is often concerned with the problem of bounding the behaviour of arbitrary finite sets in a group or ring with respect to arithmetic operations such as addition or multiplication. Similarly, combinatorial geometry…
The main result of this paper is a combinatorial description of a basis of standard level 1 module for the twisted affine Lie algebra $A_2^{(2)}.$ This description also gives two new combinatorial identities of G\"ollnitz (or…
Using representation theory techniques we prove that various spaces of derivations or one-sided multipliers over certain operator algebras are reflexive. A sample result: any bounded local derivation (local left multiplier) on an…
We study the consequences of the presence of a boundary in topological field theories in various dimensions. We characterize, univocally and on very general grounds, the field content and the symmetries of the actions which live on the…
The framework used to prove the multiplicative law deformation of the algebra of Feynman-Bender diagrams is a \textit{twisted shifted dual law} (in fact, twice). We give here a clear interpretation of its two parameters. The crossing…
We introduce an effective edge network theory to characterize the boundary topology of coupled edge states generated from various types of topological insulators. Two examples studied are a two-dimensional second-order topological insulator…
Recently the duality map between electric-like asymptotic charges of $p$-form gauge theories is studied. The outcome is an existence and uniqueness theorem and the topological nature of the duality map. The goal of this work is to extend…
This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic…
We introduce a finite-dimensional algebra that controls the possible boundary conditions of a conformal field theory. For theories that are obtained by modding out a Z_2 symmetry (corresponding to a so-called D_odd-type, or half-integer…
We describe an inner product on the diagrams on which the Temperley-Lieb algebra can be represented. We exhibit several constructions which are in natural combinatorial bijection with these diagrams, which are generalizations of various…