Abstract. Let C be the open upper light cone in R1+n with respect to the Lorentz product. The connected linear Lorentz group SOR (1, n)0 acts on C and therefore diagonally on the N -fold product T N where T = R1+n + iC ⊂ C1+n . We prove that the extended future tube SOC (1, n) · T N is a domain of holomorphy.
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