The Long-Moody construction is a method to obtain representations of braid groups introduced by Long and Moody. Also the Katz middle convolution is a method to construct local systems on the punctured Riemann sphere introduced by Katz. In this talk, it will be explain that these two methods are naturally unified and define a new functor which is called the Katz-Long-Moody functor. This functor extends the framework of Katz algorithm to categories of local systems on various topological spaces, for example, B_n-bundles associated with simple Weierstrass polynomials, complements of hyperplane arrangements of fiber-type, link complements in the solid torus, and so on.
This talk is based on a joint work with Haru Negami in Chiba University.