The Weyl group symmetry W(E-k) is studied from the points of view of the E-strings, Painleve equations and U-duality. We give a simple reformulation of the elliptic Painleve equation in such a way that the hidden symmetry W(E-10) is manifestly realized. This reformulation is based on the birational geometry of the del Pezzo surface and closely related to Seiberg-Witten curves describing the E-strings. The relation of the W(Ek) symmetry to the duality of M-theory on a torus is discussed on the level of string equations of motion. (C) 2002 Elsevier Science B.V. All rights reserved. References: 44
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