Dualities, affine vertex operator algebras, and geometry of complex polynomials
This thesis consists of two parts which deal with different subjects. In the first part we study certain aspects of the representation theory of affine Kac-Moody Lie algebras and related structures. We notice that for any positive integer k, the set of (1,2)-specialized characters of the level k standard A11-modules is the same as the set of rescaled graded dimensions of the subspaces of the level