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Lie Group Quantum Mathematics Seminar

A construction of twisted modules for grading-restricted vertex (super)algebras

Yi-Zhi Huang, Rutgers University

Location:  Hill 705
Date & time: Friday, 15 February 2019 at 12:00PM - 1:00PM

  • Abstract:  We give a general and direct construction of (grading-restricted generalized) twisted modules for a grading-restricted vertex (super)algebra V associated to an automorphism g of V. Even in the case that g is of finite order, finding such a construction has been a long-standing problem in the representation theory of vertex operator algebra and orbifold conformal field theory. Besides twisted vertex operators, one crucial ingredient in this construction is what we call the "twist vertex operators" or "twist fields." Assuming that a grading-restricted vector space W equipped with a set twisted fields and a set of twist fields satisfy a weak commutativity for twisted fields, a generalized weak commutativity for one twisted field and one twist field and a number of other properties that are relatively easy to verify, we define a twisted vertex operator map for W and prove that W equipped with this twisted vertex operator map is a (grading-restricted generalized) g-twisted V-module. As a class of examples, we construct (grading-restricted generlized) twisted moduels for vertex operator algebras associated to affine Lie algebras.

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