Dedicated to Jacques Carmona, an expert in noncommutative harmonic analysis, the volume presents excellent invited/refereed articles by top notch mathematicians. Topics cover general Lie theory, reductive Lie groups, harmonic analysis and the Langlands program, automorphic forms, and Kontsevich quantization. Good text for researchers and grad students in representation theory.

The purpose of the present memoir is two-fold. First, the authors obtain a non-abelian localization theorem when M is any even dimensional compact manifold : following an idea of E. Witten, the authors deform an elliptic symbol associated to a Clifford bundle on M with a vector field associated to a moment map. Second, the authors use this general approach to reprove the $[Q,R] = 0$ theorem of Meinrenken-Sjamaar in the Hamiltonian case and obtain mild generalizations to almost complex manifolds. This non-abelian localization theorem can be used to obtain a geometric description of the...