Given a positive-definite even lattice Q, one can construct a lattice vertex algebra V. An important problem in vertex algebra theory and conformal field theory is to classify the representations of the subalgebra of fixed points, known as an orbifold, corresponding to an isometry of the underlying lattice. Once the representations are known, one can calculate their characters to further study the properties of these representations.

Under certain assumptions, the orbifold representations are obtained by restriction from twisted or untwisted representations over the entire algebra V. Previously, we have described explicitly the orbifold representations in the case when the isometry of Q has order two. Currently, we are extending this work to prime order, while working out several examples with an isometry of order 3, which appear to be new examples.

In this talk, I will describe the notions of a lattice vertex algebra and orbifold, and describe the details of our procedure to calculate the irreducible characters for an orbifold of a lattice vertex algebra. I will also demonstrate our procedure using as examples a root lattice together with a Dynkin diagram automorphism.