Nonlocal extended conformal algebras associated with multiconstraint KP hierarchy and their free field realizations

Abstract

We study the conformal properties of the multiconstraint KP hierarchy and its nonstandard partner by covariantizing their corresponding Lax operators. The associated second Hamiltonian structures turn out to be nonlocal extensions of W-n algebra by some integer or half-integer spin fields depending on the order of the Lax operators. In particular, we show that the complicated second Hamiltonian structure of the nonstandard multiconstraint KP hierarchy can be simplified by factorizing its Lax operator to multiplication form. We then diagonalize this simplified Poisson matrix and obtain the free held realizations of its associated nonlocal algebras.