Representation Theory and Complex Analysis: Lectures given at the C.I.M.E. Summer School held in Venice, Italy, June 10-17, 2004 (Lecture Notes in Mathematics Book 1931)

Six leading experts lecture on a wide spectrum of recent results on the subject of the title, providing both a solid reference and deep insights on current research activity. __Michael Cowling__ presents a survey of various interactions between representation theory and harmonic analysis on semisimple groups and symmetric spaces. __Alain Valette__ recalls the concept of amenability and shows how it is used in the proof of rigidity results for lattices of semisimple Lie groups. __Edward Frenkel__ describes the geometric Langlands correspondence for complex algebraic curves, concentrating on the ramified case where a finite number of regular singular points is allowed. __Masaki Kashiwara__ studies the relationship between the representation theory of real semisimple Lie groups and the geometry of the flag manifolds associated with the corresponding complex algebraic groups. __David Vogan__ deals with the problem of getting unitary representations out of those arising from complex analysis, such as minimal globalizations realized on Dolbeault cohomology with compact support. __Nolan Wallach__ illustrates how representation theory is related to quantum computing, focusing on the study of qubit entanglement. Front Matter....Pages I-XII Applications of Representation Theory to Harmonic Analysis of Lie Groups (and Vice Versa)....Pages 1-50 Ramifications of the Geometric Langlands Program....Pages 51-135 Equivariant Derived Category and Representation of Real Semisimple Lie Groups....Pages 137-234 Amenability and Margulis Super-Rigidity....Pages 235-258 Unitary Representations and Complex Analysis....Pages 259-344 Quantum Computing and Entanglement for Mathematicians....Pages 345-376 Back Matter....Pages 377-388 Six leading experts lecture on a wide spectrum of recent results on the subject of the title. They present a survey of various interactions between representation theory and harmonic analysis on semisimple groups and symmetric spaces, and recall the concept of amenability. They further illustrate how representation theory is related to quantum computing; and much more. Taken together, this volume provides both a solid reference and deep insights on current research activity.