Related papers: A Note on Representations of the $w_\infty$ Algebr…
In this paper we discuss the uniqueness of the unitary representations of the non commutative Heisenberg-Weyl algebra. We show that, apart from a critical line for the non commutative position and momentum parameters, the Stone-von Neumann…
We determine the representation-finiteness of $A\otimes B$, where both $A$ and $B$ are simply connected algebras with at least three simple modules.
The groups of automorphisms of the Witt $W_n$ and Virasoro Lie algebras are found.
Suppose $\mathcal{T}_{+}(E)$ is the tensor algebra of a $W^{*}$-correspondence $E$ and $H^{\infty}(E)$ is the associated Hardy algebra. We investigate the problem of extending completely contractive representations of $\mathcal{T}_{+}(E)$…
We define a map from the set of conjugacy classes of a Weyl group W to the representation ring of W tensored with the ring of polynomials in one variable.
In this article, we provide an overview of a one-to-one correspondence between representations of the generalized Clifford algebra $C_f$ of a ternary cubic form $f$ and certain vector bundles (called Ulrich bundles) on a cubic surface $X$.…
The loop equations in the $U(N)$ lattice gauge theory are represented in the form of constraints imposed on a generating functional for the Wilson loop correlators. These constraints form a closed algebra with respect to commutation. This…
We describe all irreducible conformal subalgebras of Cend_N. The classification of simple and semisimple associative conformal algebras with finite faithful representation follows from this description.
We classify all finite growth representations of all infinite rank subalgebras of the Lie conformal algebra gc_1 that contain a Virasoro subalgebra.
We introduce representations of the Cuntz algebra $\con$ which are parameterized by sequences in the set of unit vectors in ${\bf C}^{N}$. These representations are natural generalizations of permutative representations by…
The polynomial deformations of the Witten extensions of the U(su(2)) and U(osp(1,2)) algebras are three generator algebras with normal ordering, admitting a two generator subalgebra. The modules and the representations of these algebras are…
We relate extensions of completely unitary VOAs and (commutative) Q-systems. As an application, we show that any unitary extension of a completely unitary VOA is completely unitary.
The complete structure of the Casimir ${\cal{W}\cal{A}}_{\it{N}}$ algebras are shown to exist in such a way that the Casimir ${\cal{W}\cal{A}}_{\it{N}}$ algebra is a kind of truncated type of $\cal{W}_{\infty}$ algebra both in the primary…
We give a review of the extended conformal algebras, known as $W$ algebras, which contain currents of spins higher than 2 in addition to the energy-momentum tensor. These include the non-linear $W_N$ algebras; the linear $W_\infty$ and…
Let $V_1 \otimes V_2$ be a tensor product of VOAs. Using Zhu theory we discuss the theory of representations of V (associative algebra, modules and fusion rules). We prove that this theory is more or less the same as representation theory…
We classify the representation type of the descent algebras of type $\A$ in the positive characteristic case. The algebras have finite representation type only for a few small degrees; otherwise, they are wild. Our main reduction method…
In this note we consider the algebra $U_q(\hat{sl}_\infty)$ and we study the category O of its integrable representations. The main motivations are applications to quantum toroidal algebras, more precisely predictions of character formulae…
We survey recent results on the representation theory of symplectic reflection algebras, focusing particularly on connections with symplectic quotient singularities and their resolutions, spaces of representations of quivers, and on…
We discuss various aspects of the representation theory of the local nets of von Neumann algebras on the circle associated with positive energy representations of the Virasoro algebra (Virasoro nets). In particular we classify the local…
The most general large ${\cal N}=4$ superconformal ${\cal W}_{\infty}$ algebra, containing in addition to the superconformal algebra one supermultiplet for each integer spin, is analysed in detail. It is found that the ${\cal W}_{\infty}$…