  In this paper we present a brief description of a ladder operator formalism
applied to orthogonal polynomials with discontinuous weights. The two
coefficient functions, A_n(z) and B_n(z), appearing in the ladder operators
satisfy the two fundamental compatibility conditions previously derived for
smooth weights. If the weight is a product of an absolutely continuous
reference weight w_0 and a standard jump function, then A_n(z) and B_n(z) have
apparent simple poles at these jumps. We exemplify the approach by taking w_0
to be the Hermite weight. For this simpler case we derive, without using the
compatibility conditions, a pair of difference equations satisfied by the
diagonal and off-diagonal recurrence coefficients for a fixed location of the
jump. We also derive a pair of Toda evolution equations for the recurrence
coefficients which, when combined with the difference equations, yields a
particular Painleve IV.
