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 (refered to as the (n,m)--th KdV hierarchy). The W--algebra associated to the \shs\, of the (n,m)--th KdV hierarchy (called W(n,m) algebra) is linked to the direct sum of W_m--algebra and W_{n+m}--algebra, as well as an additional U(1) current algebra by a Miura map, in turn, from the latter, we can always construct a representation of W_\infty--algebra.
展开▼
