The Long-Moody construction is a method to obtain representations of braid groups introduced by Long and Moody. Also the Katz middle convolution is known to be a method to construct local systems on $\mathbb{ C}\backslash\{ n\text{ -points}\}$ introduced by Katz. In this paper, we explain that these two methods are naturally unified and define a new functor which we call 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.
Categories: math.GT math.CA math.RT