THE INTEGRABLE HIERARCHY CONSTRUCTED FROM A PAIR OF KDV-TYPE HIERARCHIES AND ITS ASSOCIATED W-ALGEBRA

For any two arbitrary positive integers ''n'' and ''m'', using the m(t h) KdV hierarchy and the (n + m)(th) KdV hierarchy as building blocks, we are able to construct another integrable hierarchy (referred to as the (n,m)(th) KdV hierarchy). The W-algebra associated to the second Hamiltonian structure of the (n,m)(th) KdV hierarchy (called W(n, m) a lgebra) is isomorphic via a Miura map to the direct sum of a W-m-algeb ra, a W-n+m-algebra and an additional U(1) current algebra. In turn, f rom the latter, we can always construct a representation of a W-infini ty-algebra.