ON HYPER-KAHLER MANIFOLDS OF TYPE A(INFINITY) AND D-INFINITY

We shall use an infinite dimensional hyper-Kahler quotient method to o btain hyper-Kahler 4 manifolds of type A(infinity) and D-infinity. Hyp er-Kahler manifolds of type A(infinity) and D-infinity are constructed in terms of Dynkin diagrams of type A(infinity) and D-infinity respec tively A hyper-Kahler manifold of type D-infinity is the minimal resol ution of the quotient space of a hyper-Kahler manifold of type A(infin ity) by an involution. Finally we shall show that a hyper-Kahler manif old of type A(infinity) can be considered as the universal cover of el liptic fibre space of type I-b.