QM Research Seminar: Constructing unitary representation of braid group

This work establishes a correspondence between the multiplicative middle convolution of Knizhnik-Zamolodchikov (KZ)-type equations, an integral transformation that reproduces the KZ-type equation, and the Katz-Long-Moody construction, an algebraic method for constructing representations of the braid group B_n. Besides, we show that the Katz-Long-Moody construction preserves unitarity.