ON THE KADOMTSEV-PETVIASHVILI HIERARCHY, (W)OVER-CAP INFINITY ALGEBRA, AND CONFORMAL SL(2,R) U(1) MODEL .1. THE CLASSICAL CASE/

In this article the interrelationship between the integrable Kadomtsev -Petviashvili (KP) hierarchy, nonlinear W(infinity) algebra, and the c onformal noncompact SL(2,R)/U(1) coset model at the classical level is studied. The Poisson brackets of the second Hamiltonian structure of the KP hierarchy is derived first explicitly, then the W1+infinity alg ebra and its reduction W(infinity) are defined. Then it is shown that the latter is realized in the SL(2,R)/U(I.) coset model as a hidden cu rrent algebra, through a free field realization of W(infinity) in clos ed form for all higher-spin currents, in terms of two bosons. An immed iate consequence is the existence of an infinite number of KP flows in the coset model, which preserve the W(infinity)-current algebra.