Localization of free field realizations of affine Lie algebras
Vyacheslav Futorny, Dimitar Grantcharov, Renato A. Martins
TL;DR
This paper employs localization techniques to construct new irreducible modules for affine Kac-Moody algebras, specifically applying to the free field realization of A_1^{(1)} and imaginary Verma modules.
Contribution
It introduces a novel application of localization to generate irreducible modules for affine Lie algebras, expanding the understanding of their module structures.
Findings
Constructed new families of irreducible modules.
Applied localization to the free field realization of A_1^{(1)}.
Extended the module theory of affine Kac-Moody algebras.
Abstract
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 imaginary Verma modules.
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