Related papers: $W_{\infty}$ algebra in the integer quantum Hall e…
The vertex algebra W_{1+\infty,c} with central charge c may be defined as a module over the universal central extension of the Lie algebra of differential operators on the circle. For an integer n\geq 1, it was conjectured in the physics…
The algebra W_{1+\infty} with central charge c=0 can be identified with the algebra of quantum observables of a particle moving on a circle. Mathematically, it is the universal enveloping algebra of the Euclidean algebra in two dimensions.…
We show how two-dimensional incompressible quantum fluids and their excitations can be viewed as $\ W_{1+\infty}\ $ edge conformal field theories, thereby providing an algebraic characterization of incompressibility. The Kac-Radul…
Let $\D$ be the Lie algebra of regular differentialoperators on ${\C} \setminus \{0\}$, and ${\hD}= {\D} + {\C} C$ be the central extension of ${\D}$. Let $W_{1+\infty,-N}$ be the vertex algebra associated to the irreducible vacuum…
The Lie superalgebra SD of regular differential operators on the super circle has a universal central extension \hat{SD}. For each c\in C, the vacuum module M_c(\hat{SD}) of central charge c admits a vertex superalgebra structure, and…
We have generalized recent results of Cappelli, Trugenberger and Zemba on the integer quantum Hall effect constructing explicitly a ${\cal W}_{1+\infty}$ for the fractional quantum Hall effect such that the negative modes annihilate the…
We provide a generators and relation description of the deformed W_{1+\infty}-algebra introduced in previous joint work of E. Vasserot and the second author. This gives a presentation of the (spherical) cohomological Hall algebra of the…
We present the nontrivial $W_{1+\infty}$ $n$-algebra and analyze its remarkable properties. We investigate the $W_{1+\infty}$ $n$-algebra in the Landau problem and discuss the realization of the classical $w_{\infty}$ 3-algebra.…
In this thesis, we consider several aspects of over-extended and very-extended Kac-Moody algebras in relation with theories of gravity coupled to matter. In the first part, we focus on the occurrence of KM algebras in the cosmological…
It is shown that the $W_{1+\infty}$ algebra is nothing but the simplest subalgebra of a $q$-discretized \vi\ algebra, in the language of the KP hierarchy explicitly.
We propose a series of new subalgebras of the $W_{1+\infty}$ algebra parametrized by polynomials $p(w)$, and study their quasifinite representations. We also investigate the relation between such subalgebras and the…
We introduce a quantum model for the Universe at its early stages, formulating a mechanism for the expansion of space and matter from a quantum initial condition, with particle interactions and creation driven by algebraic extensions of the…
We extend the $\imath$Hall algebra realization of $\imath$quantum groups arising from quantum symmetric pairs, which establishes an injective homomorphism from the universal $\imath$quantum group of Kac-Moody type to the $\imath$Hall…
In this paper, we construct the $W_{1+\infty}$-n-algebras in the framework of the generalized quantum algebra. We characterize the $\mathcal{R}(p,q)$-multi-variable $W_{1+\infty}$-algebra and derive its $n$-algebra which is the generalized…
Quantum Hall universality classes can be classified by $W_{1+\infty}$ symmetry. We show that this symmetry also governs the dynamics of quantum edge excitations. The Hamiltonian of interacting electrons in the fully-filled first Landau…
In our paper~\cite{KR} we began a systematic study of representations of the universal central extension $\widehat{\Cal D}\/$ of the Lie algebra of differential operators on the circle. This study was continued in the paper~\cite{FKRW} in…
We discuss how a large class of incompressible quantum Hall states can be characterized as highest weight states of different representations of the \Winf algebra. Second quantized expressions of the \Winf generators are explicitly derived…
We extend our $\imath$Hall algebra construction from acyclic to arbitrary $\imath$quivers, where the $\imath$quiver algebras are infinite-dimensional 1-Gorenstein in general. Then we establish an injective homomorphism from the universal…
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 investigate a deformation of $w_{1+\infty}$ algebra recently introduced in arxiv:2111.11356 in the context of Celestial CFT that we denote by $\widetilde{W}_{1+\infty}$ algebra. We obtain the operator product expansions of the generating…