Abstract:  Haisheng Li showed that given a module (W, Y_W(\cdot, x)) for a vertex algebra (V, Y (\cdot, x)), one can obtain a new V-module W^{\Delta}= (W, Y_W(\Delta(x)\cdot, x)) if \Delta(x) satisfies certain natural conditions. Li presented a collection of such \Delta-operators for V=L(k, 0) (a vertex operator algebra associated with an affine Lie algebra, k a positive integer). In a joint paper with Bill Cook, for each irreducible L(k, 0)-module W, I find a highest weight vector of W^{\Delta} when \Delta is associated with a minuscule coweight. From this we completely determine the action of these \Delta-operators on the set of isomorphism equivalence classes of L(k, 0)-modules.

Abstract:  Twisted modules associated to a finite order automorphism for a vertex operator algebra V are well known and have been studied in detail. In a recent work, Yi-Zhi Huang introduced a more general theory of twisted modules for a vertex operator algebra, namely those associated to an arbitrary automorphism. Huang also gave a general theorem for constructing these twisted modules. In this talk, I give various examples of these constructions with certain desirable properties in the affine Lie algebra case, as well as draw a connection between these constructions and those in my previous work with William Cook.