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We overview symmetries of string scattering amplitudes in the high energylimits of both the fixed angle or Gross regime (GR) and the fixed momentumtransfer or Regge regime (RR). We calculated high energy string scatteringamplitudes (SSA) at arbitrary mass levels for both regimes. We discovered theinfinite linear relations among fixed angle string amplitudes and the infiniterecurrence relations among Regge string amplitudes. The linear relations weobtained in the GR corrected the saddle point calculations by Gross, Gross andMende. In addition, for the high energy closed string scatterings, our resultsdiffer from theirs by an oscillating prefactor which was crucial to recover theKLT relation valid for all energies. We showed that all the high energy stringamplitudes can be solved by the linear or recurrence relations so that all thestring amplitudes can be expressed in terms of a single string amplitude. Wefurther found that, at each mass level, the ratios among the fixed angleamplitudes can be extracted from the Regge string scattering amplitudes.Finally, we review the recent developments on the discovery of infinite numberof recurrence relations valid for all energies among Lauricella SSA. Thesymmetries or relations among SSA at various limits obtained previously can beexactly reproduced. It leads us to argue that the known SL(K+3,C) dynamicalsymmetry of the Lauricella function maybe crucial to probe spacetime symmetryof string theory.

Overview on High energy String Scattering Amplitudes and Symmetries of String Theory