Stringy Symmetries and Their High-energy Limit

The high-energy limit of stringy symmetries, derived from the decoupling of two types of zero-norm states in the old covariant first quantized (OCFQ) spectrum of open bosonic string, are used to reproduce Gross's linear relations among high-energy scattering amplitudes of different string states with the same momenta. Moreover, the proportionality constants between scattering amplitudes of different string states are calculated for the first few low-lying levels. These proportionality constants are, as suggested by Gross from the saddle point calculation of high-energy string-loop amplitudes, independent of the scattering angle $\phi_{CM}$ and the order $\chi$ of string perturbation theory. The decoupling of degenerate positive-norm states, which is valid to \QTR{it}{all} energy, can also be derived from these stringy symmetries. The high-energy limit of this decoupling is found to be consistent with the work of Gross and Manes.