On twisted representations of vertex algebras

In this paper we develop a formalism for working with twisted realizations of vertex and conformal algebras. As an example, we study realizations of conformal algebras by twisted formal power series. The main application of our technique is the construction of a very large family of representations for the vertex superalgebra \goth V_\Lambda corresponding to an integer lattice $\Lambda$. For an automorphism \^\sigma:\goth V_\Lambda\to\goth V_\Lambda coming from a finite order automorphism $\sigma:\Lambda \to \Lambda$ we define a category $\cal O_{\^\sigma}$ of twisted representations of \goth V_\Lambda and show that this category is semisimple with finitely many isomorphism classes of simple objects.Comment: Some corrections and addition

New Irreducible Modules for Heisenberg and Affine Lie Algebras

We study $\mathbb Z$-graded modules of nonzero level with arbitrary weight multiplicities over Heisenberg Lie algebras and the associated generalized loop modules over affine Kac-Moody Lie algebras. We construct new families of such irreducible modules over Heisenberg Lie algebras. Our main result establishes the irreducibility of the corresponding generalized loop modules providing an explicit construction of many new examples of irreducible modules for affine Lie algebras. In particular, to any function $\phi:\mathbb N\rightarrow \{\pm\}$ we associate a $\phi$-highest weight module over the Heisenberg Lie algebra and a $\phi$-imaginary Verma module over the affine Lie algebra. We show that any $\phi$-imaginary Verma module of nonzero level is irreducible.Comment: 18 page