Irreducibility and Cuspidality -- On Liftings of Holomorphic Modular Forms -- Multiplicity-free Theorems of the Restrictions of Unitary Highest Weight Modules with respect to Reductive Symmetric Pairs -- The Rankin-Selberg Method for Automorphic Distributions -- Langlands Functoriality Conjecture and Number Theory -- Discriminant of Certain K3 Surfaces.

This volume addresses the interplay between representation theory and automorphic forms. The invited papers, written by leading mathematicians, track recent progress in the ever expanding fields of representation theory and automorphic forms, and their association with number theory and differential geometry. Representation theory relates to number theory through the Langlands program, which conjecturally connects algebraic extensions of number fields to automorphic representations and L-functions. These are the subject of several of the papers. Multiplicity-free representations constitute another subject, which is approached geometrically via the notion of visible group actions on complex manifolds. Both graduate students and researchers will find inspiration in this volume. Contributors: T. Ikeda, T. Kobayashi, S. Miller, D. Ramakrishnan, W. Schmid, F. Shahidi, K. Yoshikawa