Related papers: Boundary algebras and Kac modules for logarithmic …
Given a critical quantum spin chain with a microscopic Lie-group symmetry, corresponding e.g. to $U(1)$ or $SU(2)$ spin isotropy, we numerically investigate the emergence of Kac-Moody symmetry at low energies and long distances. In that…
In vertex algebra theory, fusion rules are described as the dimension of the vector space of intertwining operators between three irreducible modules. We describe fusion rules in the category of weight modules for the Weyl vertex algebra.…
This article gives a complete account of the modular properties and Verlinde formula for conformal field theories based on the affine Kac-Moody algebra sl(2) at an arbitrary admissible level k. Starting from spectral flow and the structure…
We prove a local limit theorem for Lipschitz continuous observables on a weakly coupled lattice of piecewise expanding interval maps. The core of the paper is a proof that the spectral radii of the Fourier-transfer operators for such a…
In the context of Conformal Field Theory (CFT), many results can be obtained from the representation theory of the Virasoro algebra. While the interest in Logarithmic CFTs has been growing recently, the Virasoro representations…
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…
Based on symmetry principles, we derive a fusion algebra generated from repeated fusions of the irreducible modules appearing in the W-extended logarithmic minimal model WLM(p,p'). In addition to the irreducible modules themselves, closure…
Using simple modules over the derivation Lie algebra $C[t]\frac{d}{d t}$ of the associative polynomial algebra $C[t]$, we construct new weight Virasoro modules with all weight spaces infinite dimensional. We determine necessary and…
This thesis is concerned with aspects of the integrable Temperley--Lieb loop (TL($n$)) model on a vertically infinite lattice with two non-trivial boundaries. When $n=1$ the ground state eigenvector of the transfer matrix of this model can…
After giving some definitions for vertex operator SUPERalgebras and their modules, we construct an associative algebra corresponding to any vertex operator superalgebra, such that the representations of the vertex operator algebra are in…
Certain deformable families of vertex algebras acquire at a limit of the deformation parameter a large center, similar to affine Lie algebras at critical level. Then the vertex algebra and its representation category become a bundle over…
We study some non-highest weight modules over an affine Kac-Moody algebra at non-critical level. Roughly speaking, these modules are non-commutative localizations of some non-highest weight "vacuum" modules. Using free field realization, we…
We consider A-series modular invariant Virasoro minimal models on the upper half plane. From Lewellen's sewing constraints a necessary form of the bulk and boundary structure constants is derived. Necessary means that any solution can be…
Let $L(-{1/2}(l+1),0)$ be the simple vertex operator algebra associated to an affine Lie algebra of type $A_{l}^{(1)}$ with the lowest admissible half-integer level $-{1/2}(l+1)$, for even l. We study the category of weak modules for that…
The Virasoro logarithmic minimal models were intensively studied by several groups over the last ten years with much attention paid to the fusion rules and the structures of the indecomposable representations that fusion generates. The…
Previously we gave a proof of the Feigin--Fuchs character formula for the irreducible unitary discrete series of the Virasoro algebra with 0<c<1. The proof showed directly that the mutliplicity space arising in the coset construction of…
We present a relationship between the Calogero-Moser particles confined in harmonic oscillator potentials and a representation theory of the infinite dimensional Lie algebra which is a semi-direct sum of Virasoro algebra and its module.…
Tensor hierarchy algebras are infinite-dimensional generalisations of Cartan-type Lie superalgebras. They are not contragredient, exhibiting an asymmetry between positive and negative levels. These superalgebras have been a focus of…
We consider exceptional vertex operator algebras for which particular Casimir vectors constructed from the primary vectors of lowest conformal weight are Virasoro descendants of the vacuum. We discuss constraints on these theories that…
We extend the well-known Katznelson-Tzafriri theorem, originally posed for power-bounded operators, to the case of Ces\`aro bounded operators of any order $\alpha>0.$ For this purpose, we use a functional calculus between a new class of…