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In this review we propose a new perspective to demonstrate Gross conjectureon high energy symmetry of string theory. We review the construction of theexact string scattering amplitudes (SSA) of three tachyons and one arbitrarystring state, or the Lauricella SSA (LSSA), in the 26D open bosonic stringtheory. These LSSA form an infinite dimensional representation of the SL(K+3,C)group. Moreover, we show that the SL(K+3,C) group can be used to solve all theLSSA and express them in terms of one amplitude. As an application in the hardscattering limit, the LSSA can be used to directly prove Gross conjecture whichwas previously corrected and proved by the method of decoupling of zero normstates (ZNS). Finally, the exact LSSA can be used to rederive the recurrencerelations of SSA in the Regge scattering limit with associated SL(5,C) symmetryand the extended recurrence relations (including the mass and spin dependentstring BCJ relations) in the nonrelativistic scattering limit with associatedSL(4,C) symmetry discovered recently.

Recent developments of the Lauricella string scattering amplitudes and their exact SL(K+3,C) Symmetry