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Abstract: We study the relation between the instanton counting on ALE spaces and the BPS state counting on a toric Calabi-Yau three-fold. We put a single D4-brane on a divisor isomorphic to AN−1-ALE space in the Calabi-Yau three-fold, and evaluate the discrete changes of BPS partition function of D4-D2-D0 states in the wall-crossing phenomena. In particular, we find that the character of affine SU(N) algebra naturally arises in wall-crossings of D4-D2-D0 states. Our analysis is completely based on the wall-crossing formula for the d = 4,N = 2 supersymmetric theory obtained by dimensionally reducing the Calabi-Yau three-fold. ∗nishinak [at] post.kek.jp †yamaguch [at] het.phys.sci.osaka-u.ac.jp ar X i