Contents Preface ix Expository Papers 1 The Plancherel Formula, the Plancherel Theorem, and the Fourier Transform of Orbital Integrals Rebecca A. Herb and Paul J. Sally, Jr. 3 Branching Problems of Zuckerman Derived Functor Modules Toshiyuki Kobayashi 23 Chiral Equivariant Cohomology of Spheres Bong H. Lian, Andrew R. Linshaw, and Bailin Song 41 Research Papers 77 Computing Global Characters Jeffrey Adams 79 Stable Combinations of Special Unipotent Representations Dan M. Barbasch and Peter E. Trapa 113 Levi Components of Parabolic Subalgebras of Finitary Lie Algebras Elizabeth Dan-Cohen and Ivan Penkov 129 On Extending the Langlands-Shahidi Method to Arithmetic Quotients of Loop Groups Howard Garland 151 The Measurement of Quantum Entanglement and Enumeration of Graph Coverings Michael W. Hero, Jeb F. Willenbring, and Lauren Kelly Williams 169 The Dual Pair (Op,q, OSp2,2) and Zuckerman Translation Dan Lu and Roger Howe 183 On the Algebraic Set of Singular Elements in a Complex Simple Lie Algebra Bertram Kostant and Nolan Wallach 215 An Explicit Embedding of Gravity and the Standard Model in E8 A. Garrett Lisi 231 From Groups to Symmetric Spaces George Lusztig 245 vii

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