• Corpus ID: 14576943

Intermediate Wakimoto modules for affine sl ( n + 1 , C )

@inproceedings{Saifi2004IntermediateWM,
  title={Intermediate Wakimoto modules for affine sl ( n + 1 , C )},
  author={H. Saifi and Edward Vladimir Frenkel},
  year={2004}
}
We construct certain boson-type realizations of affine sl(n + 1, C) that depend on a parameter 0 r n such that when r = 0 we get a Fock space realization appearing in [6] and when r = n they are the Wakimoto modules described in the work of Feigin and Frenkel [7]. PACS number: 02.20.Uw Mathematics Subject Classification: 17B67, 81R10 
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References

SHOWING 1-10 OF 25 REFERENCES
Fock representations of the affine Lie algebraA1(1)
The aim of this note is to show that the affine Lie algebraA1(1) has a natural family πμ, υ,v of Fock representations on the spaceC[xi,yj;i ∈ ℤ andj ∈ ℕ], parametrized by (μ,v) ∈C2. By corresponding
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
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
Fock Space Realizations of Imaginary Verma Modules
Abstract This work expands to the setting of $\widehat{\mathfrak{sl}_{n}(\mathbb{C})}$ the results of H. Jakobsen and V. Kac and independently D. Bernard and G. Felder on the realization of
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
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
Semi-infinite induction and Wakimoto modules
The purpose of this paper is to suggest the construction and study properties of semi-infinite induction, which relates to semi-infinite cohomology the same way induction relates to homology and
Axioms for a vertex algebra and the locality of quantum fields
The identities satisfied by two-dimensional chiral quantum fields are studied from the point of view of vertex algebras. The Cauchy-Jacobi identity (or the Borcherds identity) for three mutually
Vertex algebras for beginners
Preface. 1: Wightman axioms and vertex algebras. 1.1: Wightman axioms of a QFT. 1.2: d = 2 QFT and chiral algebras. 1.3: Definition of a vertex algebra. 1.4: Holomorphic vertex algebras. 2: Calculus
REPRESENTATIONS OF AFFINE KAC-MOODY ALGEBRAS AND BOSONIZATION
...
...