Intersection-number operators for curves on discs II

Let the braid group B-n act as (isotopy classes of) diffeomorphisms of an n-punctured disc D-n. Then there is an associated action of B-n on a polynomial algebra R = C[a(1),..., a(N)] and a way of representing simple closed curves on D-n as elements of R. Fix k is an element of 2N. Using this approach we show that the image in Aut(R) of each Dehn twist tau about a simple closed gamma in D-n satisfies a kind of characteristic equation when its action is restricted to the image in R of the set of curves gamma having geometric intersection number k with gamma.