Subconvexity for $G{L}_3(R)$ $L$-Functions: The Key Identity via Integral Representations

We study the subconvexity problem for $G{L}_3(R)$ $L$-functions in the t-aspect using integral representations by combining techniques employed by Michel-Venkatesh in their study of the corresponding problem for $G{L}_2$ with ideas from recent works of Munshi, Holowinsky-Nelson and Lin. Our main objective is to give - from the perspective of integral representations of $L$-functions and automorphic representation theory - a possible explanation of the origin of the “key identity” arising in the latter series of works.