INFN, Sezione di Trieste.

For any two arbitrary positive integers ‘n’ and ‘m’, using the m–th 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) algebra) is isomorphic via a Miura map to the direct sum of a Wm–algebra, a Wn+m–algebra and an additional U(1) current algebra. In turn, from the latter, we can always construct a representation of a W∞–algebra.