Abstract
In this paper, we develop a formalism for working with representations of vertex and conformal algebras by generalized fields—formal power series involving non-integer powers of the variable. The main application of our technique is the construction of a large family of representations for the vertex superalgebra V Λ corresponding to an integer lattice Λ. For an automorphism σ ̂ : V Λ→ V Λ coming from a finite-order automorphism σ : Λ→Λ we find the conditions for existence of twisted modules of V Λ . We show that the category of twisted representations of V Λ is semisimple with finitely many isomorphism classes of simple objects.
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