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Lie Groups Quantum Mathematics Seminar

A unitary tensor product theory for unitary representations of unitary vertex operator algebras

 Bin Gui, Vanderbilt University

Location:  HILL 705
Date & time: Friday, 22 September 2017 at 12:00PM - 1:00PM

  • Abstract:  A formal definition of unitary vertex operator algebras was introduced by Dong, Lin. For many examples of unitary VOAs (unitary minimal models, affine Lie algebras at non-negative integer levels), all representations are unitarizable. It is natural to ask whether their tensor product theories are unitary. In this talk, we try to answer this question. Let V be a unitary vertex operator algebra. We define a sesquilinear form on the tensor product of two unitary V-modules. We show that, when these sesquilinear forms are positive definite (i.e., when they are inner products), the modular tensor category for V is unitary. The positive definiteness of these sesquilinear forms, especially the positivity, is much harder to prove. We explain the main idea of the proof if time permitted.

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