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The extended future tube conjecture for \(SO(1,n)\). (English) Zbl 1170.32300
Summary: Let \(C\) be the open upper light cone in \(\mathbb{R}^{1+n}\) with respect to the Lorentz product. The connected linear Lorentz group \(\text{SO}_\mathbb{R}(1,n)^0\) acts on \(C\) and therefore diagonally on the \(N\)-fold product \(T_N\) where \(T=\mathbb{R}^{1+n}+iC\subset \mathbb{C}^{1+n}\). We prove that the extended future tube \(\text{SO}_\mathbb{C}(1,n)\cdot T^N\) is a domain of holomorphy.
MSC:
32A07 Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube) (MSC2010)
32D05 Domains of holomorphy
32M05 Complex Lie groups, group actions on complex spaces
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