Absolute values of L-functions for GL(n,R) at the point 1

We study the values of |L(1,F)| for Hecke-Maass cusp forms F on SL(n,Z)(n≥3) of large Langlands parameters. New unconditional results on the extreme values and conditional results on the size range are derived, which determine precisely the order of magnitude of L(1,F). In addition, we enhance the new average estimate toward the Ramanujan Conjecture due to Matz and Templier. An application of the Hecke multiplicativity to the Littlewood-Richardson rule for a product of two Schur polynomials is cultivated.