Lie Groups: Structure, Actions, and Representations

Lie Groups: Structures, Actions, and Representations, In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday consists of invited expository and research articles on new developments arising from Wolf's profound contributions to mathematics. Due to Professor Wolf's broad interests, outstanding mathematicians and scholars in a wide spectrum of mathematical fields contributed to the volume. Algebraic, geometric, and analytic methods are employed. More precisely, finite groups and classical finite dimensional, as well as infinite-dimensional Lie groups, and algebras play a role. Actions on classical symmetric spaces, and on abstract homogeneous and representation spaces are discussed. Contributions in the area of representation theory involve numerous viewpoints, including that of algebraic groups and various analytic aspects of harmonic analysis.

Contributors

D. Akhiezer T. Oshima

A. Andrada I. Pacharoni

M. L. Barberis F. Ricci

L. Barchini S. Rosenberg

I. Dotti N. Shimeno

M. Eastwood J.Tirao

V. Fischer S. Treneer

T. Kobayashi C.T.C. Wall

A. Korányi D. Wallace

B. Kostant K. Wiboonton

P. Kostelec F. Xu

K.-H. Neeb O. Yakimova

G. Olafsson R. Zierau

B. Ørsted

Invited contributions are written by distinguished researchers in the field Most articles are surveys of important research areas involving algebraic, geometric, and analytic methods Finite groups and classical finite dimensional as well as infinite-dimensional Lie groups and algebras are discussed in detail Includes supplementary material: sn.pub/extras

Contenu

Preface.- Real group orbits on flag manifolds.- Complex connections with trivial holonomy.- Indefinite harmonic theory and harmonic spinors.- Twistor theory and the harmonic hull.- Nilpotent Gelfand pairs and spherical transforms of Schwartz functions, II: Taylor expansions on singular sets.- Propagation of the multiplicity-freeness property for holomorphic vector bundles.- Poisson transforms for line bundles from the Shilov boundary to bounded symmetric domains.- Cent(U(n)), cascade of orthogonal roots, and a construction of LipsmanWolf.- Weakly harmonic Maaß forms and the principal series for SL(2,R).- Holomorphic realization of unitary representations of Banach-Lie groups.- The SegalBargmann transform on compact symmetric spaces and their direct limits.- Analysis on flag manifolds and Sobolev inequalities.- Boundary value problems on Riemannian symmetric spaces of noncompact type.- One step spherical functions of the pair (SU(n + 1), U(n)).- ChernWeil theory for certain infinite-dimensional Lie groups.- On the structure of finite groups with periodic cohomology.