• Corpus ID: 246036002

Generalized Imaginary Verma and Wakimoto modules

@inproceedings{Guerrini2022GeneralizedIV,
  title={Generalized Imaginary Verma and Wakimoto modules},
  author={Marcela Guerrini and Iryna Kashuba and Oscar Armando Hern'andez Morales and Andr{\'e} DE Oliveira and Fernando Junior Santos},
  year={2022}
}
. 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 subalgebra is infinite-dimensional and the central charge is nonzero. Our approach uniforms and generalizes all previously known results with im-posed restrictions on inducing modules. We also define generalized Imaginary Wakimoto modules which provide an explicit realization for generic generalized Imaginary… 
Affine Lie algebras representations induced from Whittaker modules
. We use induction from parabolic subalgebras with infinite-dimensional Levi factor to construct new families of irreducible representations for arbitrary Affine Kac-Moody algebra. Our first construction

References

SHOWING 1-10 OF 21 REFERENCES
Generalized Loop Modules for Affine Kac–Moody Algebras
We construct new families of irreducible modules for any affine Kac–Moody algebra by considering the parabolic induction from irreducible modules over the Heisenberg subalgebra with a nonzero central
Localization of Free Field Realizations of Affine Lie Algebras
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
Intermediate Wakimoto modules for affine sl ( n + 1 , C )
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
Fock Space Realizations of Imaginary Verma Modules
The motivation for this paper goes back to at least the work of A. Borel, R. Bott and A. Weil on their geometric construction of irreducible representations of complex simple Lie groups, and the
VERMA MODULES INDUCED FROM NONSTANDARD BOREL SUBALGEBRAS
In this paper we study composition series and em-beddings of Verma modules induced from "nonstandard" Borel subalgebras. This article can be viewed as a generalization of Futorny's work on imaginary
...
...