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Group gradings on Lie algebras and applications to geometry. II (Y. Bahturin, M. Goze, E. Remm).- Harmonic analysis on homogeneous complex bounded domains and noncommutative geometry (P. Bieliavsky, V. Gayral, A. de Goursac, F. Spinnler).- The radon transform and its dual for limits of symmetric spaces (J. Hilgert, G. Ólafsson).- Cycle Connectivity and Automorphism Groups of Flag Domains (A. Huckleberry).- Shintani functions, real spherical manifolds, and symmetry breaking operators (T. Kobayashi).- Harmonic spinors on reductive homogeneous spaces (S. Mehdi, R. Zierau).- Twisted Harish–Chandra sheaves and Whittaker modules: The nondegenerate case (D. Miličić, W. Soergel).- Unitary representations of unitary groups (K.-H. Neeb).- Weak splitting of quotients of Drinfeld and Heisenberg doubles (M. Yakimov).

<p>This volume reviews and updates a prominent series of workshops in representation/Lie theory, and reflects the widespread influence of those  workshops in such areas as harmonic analysis, representation theory, differential geometry, algebraic geometry, and mathematical physics.  Many of the contributors have had leading roles in both the classical and modern developments of Lie theory and its applications. This Work, entitled <i>Developments and Retrospectives in Lie Theor</i>y, and comprising 26 articles, is organized in two volumes: <i>Algebraic Methods</i> and <i>Geometric and Analytic Methods</i>. This is the <i>Geometric and Analytic Methods</i> volume.</p><p>The Lie Theory Workshop series, founded by Joe Wolf and Ivan Penkov and joined shortly thereafter by Geoff Mason, has been running for over two decades. Travel to the workshops has usually been supported by the NSF, and local universities have provided hospitality. The workshop talks have been seminal in describing new perspectives in the field covering broad areas of current research.  Most of the workshops have taken place at leading public and private universities in California, though on occasion workshops have taken place in Oregon, Louisiana and Utah.  Experts in representation theory/Lie theory from various parts of  the Americas, Europe and Asia have given talks at these meetings. The workshop series is robust, and the meetings continue on a quarterly basis. </p><p>Contributors to the <i>Geometric and Analytic Methods</i> volume:</p><p>Y. Bahturin                                         D. Miličić</p><p>P. Bieliavsky                                       K.-H. Neeb</p><p>V. Gayral                                            G. Ólafsson</p><p>A.de Goursac                                     E. Remm</p><p>M. Goze                                             W. Soergel</p><p>J. Hilgert                                             F. Spinnler</p><p>A. Huckleberry                                    M. Yakimov</p><p>T. Kobayashi                                       R. Zierau</p><p>S. Mehdi<br></p><p> </p>

Includes contributions by international experts in representation theory/Lie theory Contains articles covering representation theory from algebraic, geometric, analytic, and topological perspectives Reviews and updates the prominent, seminal series of Lie Theory Workshops Includes supplementary material: sn.pub/extras