Regular representations and Huang–Lepowsky tensor functors for vertex operator algebras

✍ Scribed by Haisheng Li

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 297 KB
• Volume: 255
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1016/s0021-8693(02)00137-0

✦ Synopsis

This is the second paper in a series devoted to studies of regular representations for vertex operator algebras. In this paper, given a module W for a vertex operator algebra V , we construct, from the dual space W * , a family of canonical (weak) V ⊗ V -modules called D Q(z) (W ) parameterized by a nonzero complex number z. We prove that for V -modules

in the sense of Huang and Lepowsky exactly amounts to a (W ) and that a Q(z)-tensor product of V -modules W 1 and W 2 in the sense of Huang and Lepowsky amounts to a universal from W 1 ⊗ W 2 to the functor F Q(z) , where F Q(z) is a functor from the category of V -modules to the category of weak V ⊗ V -modules defined by (W ) for a V -module W . Furthermore, Huang-Lepowsky's P (z)and Q(z)-tensor functors for the category of V -modules are extended to functors T P (z) and T Q(z) from the category of V ⊗ V -modules to the category of V -modules. It is proved that functors F P (z) and F Q(z) are right adjoints of T P (z) and T Q(z) , respectively.