Abstract
Using the tool of pseudo-difference operators, the string equation for the discrete Kadomtsev-Petviashvili (KP) hierarchy is introduced and a general expression for the string equation is formulated. Furthermore, the operators of the constraints that the string equation imposes on the tau-function of the p-reduced dKP hierarchy are presented. The algebra, which part of the constraints spans, and eigenvalues of part of the constraints corresponding to the tau-function are calculated. It is also shown that this algebra is exactly a Witt algebra not only for p = 2, but also for a general p is an element of N, and that the tau-function of the p-reduced dKP hierarchy constrained by the string equation is a vacuum vector of a Witt algebra. (C) 2013 AIP Publishing LLC.