Related papers: W-Extended Logarithmic Minimal Models

This note extends some results of a previous paper (math.RT/0403250) about finite dimensional representations of the wreath product symplectic reflection algebra H(k,c,N,G) of rank N attached to a finite subgroup G of SL(2,C) (here k is a…

Because of the importance of unitarity in quantum physics, work on the representations of the de Sitter group has focussed on the unitary case, which necessarily means infinite dimensional matrices for this non-compact group. Here we…

We introduce a new family of C_2-cofinite N=1 vertex operator superalgebras SW(m), $m \geq 1$, which are natural super analogs of the triplet vertex algebra family W(p), $p \geq 2$, important in logarithmic conformal field theory. We…

Finite versions of W-algebras are introduced by considering (symplectic) reductions of finite dimensional simple Lie algebras. In particular a finite analogue of $W^{(2)}_3$ is introduced and studied in detail. Its unitary and non-unitary,…

This paper is part of an effort to gain further understanding of 2D Logarithmic Conformal Field Theories (LCFTs) by exploring their lattice regularizations. While all work so far has dealt with the Virasoro algebra (or the product of left…

The SL(2,Z) representation $\pi$ on the center of the restricted quantum group U_{q}sl(2) at the primitive 2p-th root of unity is shown to be equivalent to the SL(2,Z) representation on the extended characters of the logarithmic (1,p)…

We classify the finite dimensional irreducible representations with integral central character of finite $W$-algebras $U(\mathfrak g,e)$ associated to standard Levi nilpotent orbits in classical Lie algebras of types B and C. This…

We study modularity of the characters of a vertex (super)algebra equipped with a family of conformal structures. Along the way we introduce the notions of rationality and cofiniteness relative to such a family. We apply the results to…

We discuss our recent results on the representation theory of $\mathcal{W}$--algebras relevant to Logarithmic Conformal Field Theory. First we explain some general constructions of $\mathcal{W}$-algebras coming from screening operators.…

Let $G$ be a semisimple Lie group. We describe the irreducible representations of $G$ by linear isometries on $L_p$-spaces for $p\in (1,+\infty)$ with $p\neq 2.$ More precisely, we show that, for every such representation $\pi,$ there…

In this paper the W-algebra W(2,2) and its representation theory are studied. It is proved that a simple vertex operator algebra generated by two weight 2 vectors is either a vertex operator algebra associated to a highest irreducible…

For a partially ordered set P, we denote by Co(P) the lattice of order-convex subsets of P. We find three new lattice identities, (S), (U), and (B), such that the following result holds. Theorem. Let L be a lattice. Then L embeds into some…

Based on invariant algebras, we introduce representations$^{6-th}$ of Lie algebras and representations$^{< 4-th>}$ of Leibniz algebras, give the extended P-B-W Theorems in the context of the new representations of Lie algebras and Leibniz…

Let E be a finite extension of Fp. Using Fontaine's theory of (phi,Gamma)-modules, Colmez has shown how to attach to any irreducible E-linear representation of Gal(Qpbar/Qp) an infinite dimensional smooth irreducible E-linear representation…

We define an integrable lattice model which, in the notation of Yang, in addition to the conventional 2-particle $R$-matrices also contains non-reducible 3-particle $R$-matrices. The corresponding modified Yang-Baxter equations are solved…

We begin a systematic study of unitary representations of minimal $W$-algebras. In particular, we classify unitary minimal $W$-algebras and make substantial progress in classification of their unitary irreducible highest weight modules. We…

In this paper we study the variety of one dimensional representations of a finite $W$-algebra attached to a classical Lie algebra, giving a precise description of the dimensions of the irreducible components. We apply this to prove a…

It is well-known that families of two-dimensional toroidal conformal field theories possess a dense subset of rational toroidal conformal field theories, which makes such families an interesting testing ground about rationality of conformal…

Let $\mathcal{W}(b)$ be a class of free Lie conformal algebras of rank $2$ with $\mathbb{C}[\partial]$-basis ${L,H}$ and relations \begin{eqnarray*} [L_\lambda L]=(\partial+2\lambda)L,\ \ [L_\lambda H]=\big(\partial+(1-b)\lambda\big)H, \ \…

First, we prove the Kac-Wakimoto conjecture on modular invariance of characters of exceptional affine W-algebras. In fact more generally we prove modular invariance of characters of all lisse W-algebras obtained through Hamiltonian…