In this note we consider the set of line operators in theories of class S. We
show that this set carries the action of a natural discrete dynamical system associated with
the BPS spectrum. We discuss several applications of this perspective; the relation with
global properties of the theory; the set of constraints imposed on the spectrum generator,
in particular for the case of SU(2) N = 2∗
; and the relation between line defects and certain
spherical Double Affine Hecke Algebras.
