Related papers: Free field realizations in representation theory a…
We review the recent development in the representation theory of the $W_{1+\infty}$ algebra. The topics that we concern are, Quasifinite representation, Free field realizations, (Super) Matrix Generalization, Structure of subalgebras such…
We find an explicit formula for the conformal vector of any quantum affine $W$-algebra in its free field realization.
The goal of the present paper is to obtain new free field realizations of affine Kac-Moody algebras motivated by geometric representation theory for generalized flag manifolds of finite-dimensional semisimple Lie groups. We provide an…
We review some aspects of the free field approach to two-dimensional conformal field theories. Specifically, we discuss the construction of free field resolutions for the integrable highest weight modules of untwisted affine Kac-Moody…
This is an introduction to the basic ideas and to a few further selected topics in conformal quantum field theory and in the theory of Kac-Moody algebras.
In this paper we consider Wakimoto free field realizations of simple affine Lie algebras, a subject already much studied. We present three new sets of results. (i) Based on quantizing differential operator realizations of the corresponding…
Talk presented by J.L. Petersen at the 29th Symposium Ahrenshop, Buckow August 29-September 2, 1995. A presentation is given of the free field realization relevant to SL(2) WZW theories with a Hilbert space based on admissible…
In this thesis steps are taken in the direction of formulating non-critical strings in the framework of the $G/G$ approach. A major part of the thesis is concerned with conformal field theory based on affine $SL(2)$ current algebra, in…
These lecture notes are a brief introduction to Wess-Zumino-Witten models, and their current algebras, the affine Kac-Moody algebras. After reviewing the general background, we focus on the application of representation theory to the…
We study quasi-finite representation of the $\Winf$ algebra recently proposed by Kac and Radul. When the central charge is integer, we show that they are represented by free fermions and bosonic ghosts. There are some nontrivial…
Free field representation for the classical limit of quantum affine algebra is constructed by simple deformation of the known expressions from WZW theory.
In a vertex algebraic framework, we present an explicit description of the twisted Wakimoto realizations of the affine Lie algebras in correspondence with an arbitrary finite order automorphism and a compatible integral gradation of a…
This is the text of the Hermann Weyl Prize lecture given by the author at the XXIV Colloquium on Group Theoretical Methods in Physics, Paris, July 2002 (to appear in the Proceedings of the Colloquium).
Some time ago, conformal data with affine fusion rules were found. Our purpose here is to realize some of these conformal data, using systems of free bosons and parafermions. The so constructed theories have an extended $W$ algebras which…
We use localization technique to construct new families of irreducible modules of affine Kac-Moody algebras. In particular, localization is applied to the first free field realization of the affine Lie algebra A_1^{(1)} or, equivalently, to…
In this paper we construct two free field realizations of the elliptic affine Lie algebra sl(2,R) + \Omega_R/dR, where R=C[t,t^{-1},u|u^2=t^3 - 2b t^2 + t]. The first realization gives an analogue of Wakimoto's construction for Affine…
We present free field realizations for the associated vertex operator algebras of a number of four-dimensional $\mathcal{N}=2$ superconformal field theories. Our constructions utilize an exceptionally small set of chiral bosons whose number…
Let G be a reductive algebraic group over a local field K or a global field F. It is well know that there exists a non-trivial and interesting representation theory of the group G(K) as well as the theory of automorphic forms on the…
These lectures consisted of an elementary introduction to conformal field theory, with some applications to statistical mechanical systems, and fewer to string theory. Contents: 1. Conformal theories in d dimensions 2. Conformal theories in…
In our earlier papers we proposed a new approach to integrable hierarchies of soliton equations and their quantum deformations. We have applied this approach to the Toda field theories and the generalized KdV and modified KdV (mKdV)…