  Classically, it is well known that a single weight on a real interval leads
to orthogonal polynomials. In "Generalized orthogonal polynomials, discrete KP
and Riemann-Hilbert problems", Comm. Math. Phys.
  207, pp. 589-620 (1999), we have shown that $m$-periodic sequences of weights
lead to "moments", polynomials defined by determinants of matrices involving
these moments and $2m+1$-step relations between them, thus leading to
$2m+1$-band matrices $L$. Given a Darboux transformations on $L$, which effect
does it have on the $m$-periodic sequence of weights and on the associated
polynomials ? These questions will receive a precise answer in this paper. The
methods are based on introducing time parameters in the weights, making the
band matrix $L$ evolve according to the so-called discrete KP hierarchy.
Darboux transformations on that $L$ translate into vertex operators acting on
the $\tau$-function.
