Representations of affine Kac-Moody algebras, bosonization and resolutions
type: Item
instance of: scholarly article
title: Representations of affine Kac-Moody algebras, bosonization and resolutions
zbMATH Open document ID: 0711.17012
DOI: 10.1007/BF00429950
author: B. Feigin
author: Edward Frenkel
published in: Letters in Mathematical Physics
publication date: 1990-01-01T00:00:00Z
review text: The Fock space over the infinite Heisenberg algebra can be made into a two-parameter module over the Virasoro algebra. This family of two- parameter modules contains certain submodules, chains, which from a physical point of view are primary fields while the intertwining operators yield the screening operators. These operators allow one to construct a representation of correlation functions of some 2-dimensional statistical models (on the plane and torus). The authors study boson representations of affine Kac-Moody algebras -- certain highest weight modules called Wakimoto modules and with their help they explicitly describe primary fields and, using vertex operators, the intertwining operators. A resolution of an irreducible Wakimoto module similar to the BGG-resolution is given and certain semi-infinite cohomologies of the nilpotent subalgebra (of the considered Kac-Moody algebra) are calculated. All these give new procedures for bosonization of Wess-Zumino-Witten models and the integral representation of correlation functions in WZW models on the plane and the torus.
Mathematics Subject Classification ID: 17B67
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 81T10
zbMATH DE Number: 4168906
zbMATH Keywords: boson representations
zbMATH Keywords: affine Kac-Moody algebras
zbMATH Keywords: highest weight modules
zbMATH Keywords: Wakimoto modules
zbMATH Keywords: primary fields
zbMATH Keywords: intertwining operators
zbMATH Keywords: semi-infinite cohomologies
zbMATH Keywords: Wess-Zumino-Witten models
zbMATH Keywords: integral representation of correlation functions
reviewed by: Dimitry Leites
MaRDI profile type: Publication
cites work: Fock space representations of the Virasoro algebra. Intertwining operators
cites work: Fock representations of the affine Lie algebra \(A_ 1^{(1)}\)
cites work: Infinite dimensional Lie algebras. An introduction
cites work: Homogeneous vector bundles
cites work: Structure of representations with highest weight of infinite-dimensional Lie algebras
cites work: The Grothendieck-Cousin complex of an induced representation
cites work: Morse theory for fixed points of symplectic diffeomorphisms
cites work: Modular invariant representations of infinite-dimensional Lie algebras and superalgebras
description: scientific article; zbMATH DE number 4168906