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Lie Group Quantum Mathematics Seminar

Twisted intertwining operators and tensor products of (generalized) twisted modules

Jishen Du

Location:  Hill 705
Date & time: Friday, 26 April 2024 at 12:10PM - 1:10PM

It is known that the notion of vertex/intertwining operator defined using formal variables and Jacobi identity has an equivalent definition using complex analytic approach. When studying orbifold theory, even for one twisted intertwining operator among twisted modules, it is necessary to use the complex analytic approach. Using the complex analytic approach, we introduce a more general notion of twisted intertwining operator, and prove basic properties. We introduce a notion of P(z)-tensor product of two twisted modules and give a construction of such a P(z)-tensor product under suitable assumptions. We formulate a P(z)-compatibility condition and a P(z)-grading-restriction condition and used these conditions to give another construction of the P(z)-tensor product, which is expected to be useful to construct a G-crossed braided tensor category from a VOA and a group G of automorphisms of the VOA.

This work is joint with my advisor, Prof. Yi-Zhi Huang.