Principal subspaces of twisted modules for certain lattice vertex operator algebras

Christopher Sadowski (Collegeville, PA)

Abstract

In this talk, we give a survey of some results in the study of principal subspaces of twisted modules for certain lattice vertex operator algebras. Namely, we will discuss the structure of the principal subspaces for the basic modules for Lie algebras of types $A_{n}^{(2)}, D_n^{(2)}, D_4^{(3)}$, and $E_6^{(2)}$, as well as extensions of this work to twisted modules for more general lattice vertex operator algebras. We also discuss some recent observations which connect the graded-dimensions of these principal subspaces to various $q$-series identities.