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We investigate the Seiberg-Witten monopole equations on noncommutative(N.C.)R^4 at the large N.C. parameter limit, in terms of the equivariant cohomology.In other words, N}=2 supersymmetric U(1) gauge theories with hypermultiplet onN.C. R}^4 are studied. It is known that after topological twisting partitionfunctions of N}>1 supersymmetric theories on N.C. R^2D are invariant underN.C.parameter shift, then the partition functions can be calculated by itsdimensional reduction. At the large N.C. parameter limit, the Seiberg-Wittenmonopole equations are reduced to ADHM equations with the Dirac equationreduced to 0 dimension. The equations are equivalent to the dimensionalreduction of non-Abelian U(N) Seiberg-Witten monopole equations in N -> \infty.The solutions of the equations are also interpreted as a configuration of braneanti-brane system. The theory has global symmetries under torus actionsoriginated in space rotations and gauge symmetries. We investigate theSeiberg-Witten monopole equations reduced to 0 dimension and the fixed pointequations of the torus actions. We show that the Dirac equation reduced to 0dimension is trivial when the fixed point equations and the ADHM equations aresatisfied. For finite N, it is known that the fixed points of the ADHM data areisolated and are classified by the Young diagrams. We give a new proof of thisstatement by solving the ADHM equations and the fixed point equationsconcretely and by giving graphical interpretations of the field components andthese equations.Comment: v2: 28+1 pages, 13 figures, appendix for convention added, references  added, some descriptions improved, v3: eq.(113),(117) corrected, v4: 29+1  pages, minor correction

Dimensional reduction of Seiberg-Witten monopole equations, N=2 noncommutative supersymmetric field theories and Young diagrams