engleski

On logarithmic modules for affine vertex operator algebras

We shall first review basic results for logarithmic modules for vertex operator algebras and discuss methods for their constructions. Then we present recent explicit realizations of certain affine vertex algebras and discuss their applications in the representation theory. Admissible affine vertex operator algebras $V_{;k}; (\mathfrak g)$ are semi-simple in the category $\mathcal O$. In this talk, we shall consider $V_{;k}; (\mathfrak g)$--modules outside of the category $\mathcal O$. Logarithmic modules appear in the non-split extension of certain weight modules. Although $V_{;k}; (\mathfrak g)$--modules are modules for the affine Lie algebras, it is difficult to construct indecomposable and logarithmic modules using concepts from the representation theory of Lie algebras. We will show how these modules can be explicitly constructed using vertex-algebraic techniques. We also study a connection with triplet vertex algebras.

Logarithmic modules ; affine vertex algebra

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