### 学术报告: On logarithmic modules for affine vertex operator algebras

University of Zagreb

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..