Localization of Free Field Realizations of Affine Lie Algebras

  title={Localization of Free Field Realizations of Affine Lie Algebras},
  author={Vyacheslav Futorny and Dimitar Grantcharov and Renato A. Martins},
  journal={Letters in Mathematical Physics},
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 $${A_{1}^{(1)}}$$A1(1) or, equivalently, to imaginary Verma modules. 
5 Citations
Generalized Imaginary Verma and Wakimoto modules
. We develop a general technique of constructing new irreducible weight modules for any affine Kac-Moody algebra using the parabolic induction, in the case when the Levi factor of a parabolic
Module structure on $U(\mathfrak{h})$ for Kac-Moody algebras
Let $\g$ be an arbitrary Kac-Moody algebra with a Cartan sualgebra $\h$. In this paper, we determine the category of $\g$-modules that are free $U(\h)$-modules of rank 1.
Irreducible A1(1)-modules from modules over two-dimensional non-abelian Lie algebra
For any module V over the two-dimensional non-abelian Lie algebra b and scalar α ∈ C, we define a class of weight modules Fα(V) with zero central charge over the affine Lie algebra A1(1). These
Module structures on $\bm{U(\h)}$ for Kac-Moody algebras
Let $\g$ be an arbitrary Kac-Moody algebra with a Cartan subalgebra $\h$. In this paper, we determine the category of $\g$-modules that are free $U(\h)$-modules of rank 1. More precisely, this


Imaginary Verma Modules for Affine Lie Algebras
  • V. Futorny
  • Mathematics
    Canadian Mathematical Bulletin
  • 1994
Abstract We study a class of irreducible modules for Affine Lie algebras which possess weight spaces of both finite and infinite dimensions. These modules appear as the quotients of "imaginary Verma
Classification of Irreducible Nonzero Level Modules with Finite-Dimensional Weight Spaces for Affine Lie Algebras
Abstract We classify the irreducible weight affine Lie algebra modules with finite-dimensional weight spaces on which the central element acts nontrivially. In particular, we show that any such
Explicit Realizations of Simple Weight Modules of Classical Lie Superalgebras
We prove that every simple weight module with finite weight multiplicities of a simple classical Lie superalgebra is isomorphic to a twisted localization of a highest weight module.
A Family of Irreducible Representations of the Witt Lie Algebra with Infinite-Dimensional Weight Spaces
We define a 4-parameter family of generically irreducible and inequivalent representations of the Witt Lie algebra on which the infinitesimal rotation operator acts semisimply with
Affine Kac-Moody algebras and semi-infinite flag manifolds
We study representations of affine Kac-Moody algebras from a geometric point of view. It is shown that Wakimoto modules introduced in [18], which are important in conformal field theory, correspond
Algebraic construction of contragradient quasi-Verma modules in positive characteristic
In the present paper we investigate a new class of infinite-dimensional modules over the hyperalgebra of a semi-simple algebraic group in positive chararacteristic called quasi-Verma modules. We
Fock representations and BRST cohomology inSL(2) current algebra
We investigate the structure of the Fock modules overA1(1) introduced by Wakimoto. We show that irreducible highest weight modules arise as degree zero cohomology groups in a BRST-like complex of