  Based on the idea of symmetric constraint, we apply the Gesztesy-Holden's
method to derive explicit representations of the Baker-Ahkiezer function
$\psi_1$ of the KP hierarchy, from which we provide theta function
representations of algebro-geometric solutions for the whole
Kadomtsev-Petviashvili (KP) hierarchy. This provides a approach to obtain some
special subclasses of algebro-geometric solutions for the KP hierarchy and
other high dimensional hierarchy of equations.
