CONTENTS -- Foreword -- Preface -- The Theta Correspondence over R Jeffrey Adams -- 1. Introduction -- 2. Fock Model: Complex Lie Algebra -- 3. Schrodinger Model -- 4. Fock Model: Real Lie Algebra -- 5. Duality -- 6. Compact Dual Pairs -- 7. Joint Harmonics -- 8. Induction Principle -- 9. Examples -- References -- The Heisenberg Group, SL(3 -- R), and Rigidity Andreas Cap, Michael G. Cowling, Filippo De Mari, Michael Eastwood and Rupert McCallum -- 1. Introduction -- 2. An Example -- 3. Related Questions in Two Dimensions -- 4. Proof of Theorem 2.1 -- 5. Final Remarks -- References -- Pfafflans and Strategies for Integer Choice Games Ron Evans and Nolan Wallach -- 1. Introduction -- 2. Strategies for the Multivariate Game -- 3. Strategies for the Single Variable Game -- 4. Strategies for Some Constricted Multivariate Games -- 5. Appendix: Pfa ans Associated with Payo Matrices -- References -- When is an L-Function Non-Vanishing in Part of the Critical Strip? Stephen Gelbart -- Introduction -- 1. The Classical Method -- 2. The Rankin-Selberg Generalization of de la Vall ee Poussin -- 3. An Approach Using Eisenstein Series on SL(2 -- R) -- 4. The General Method -- References -- Cohomological Automorphic Forms on Unitary Groups, II: Period Relations and Values of L-Functions Michael Harris -- Introduction -- Errors and Misprints in [H4] -- 0. Preliminary Notation -- 1. Eisenstein Series on Unitary Similitude Groups -- 2. The Local Theta Correspondence -- Appendix. Generic Calculation of the Unrami ed Correspondence -- 3. Applications to Special Values of L-Functions -- 4. Applications to Period Relations -- The Inversion Formula and Holomorphic Extension of the Minimal Representation of the Conformal Group Toshiyuki Kobayashi and Gen Mano -- Contents -- 1. Introduction -- 1.1. Semigroup generated by a differential operator D.

1.2. Comparison with the Hermite operator D -- 1.3. The action of SL(2 -- R) O(m) -- 1.4. Minimal representation as hidden symmetry -- 2. Preliminary Results on the Minimal Representation of O(m + 1 -- 2) -- 2.1. Maximal parabolic subgroup of the conformal group -- 2.2. L2-model of the minimal representation -- 2.3. K-type decomposition -- 2.4. Infinitesimal action of the minimal representation -- 3. Branching Law of + -- 3.1. Schr odinger model of the minimal representation -- 3.2. K- nite functions on the forward light cone C+ -- 3.3. Description of in nitesimal generators of sl(2 -- R) -- 3.4. Central element Z of kC -- 3.5. Proof of Proposition 3.2.1 -- 3.6. One parameter holomorphic semigroup (etZ ) -- 4. Radial Part of the Semigroup -- 4.1. Result of the section -- 4.2. Upper estimate of the kernel function -- 4.3. Proof of Theorem 4.1.1 (Case Re t > 0) -- 4.4. Proof of Theorem 4.1.1 (Case Re t = 0) -- 4.5. Weber's second exponential integral formula -- 4.6. Dirac sequence operators -- 5. Integral Formula for the Semigroup -- 5.1. Result of the section -- 5.2. Upper estimates of the kernel function -- 5.3. Proof of Theorem 5.1.1 (Case Re t > 0) -- 5.4. Proof of Theorem 5.1.1 (Case Re t = 0) -- 5.5. Spectra of an O(m)-invariant operator -- 5.6. Proof of Lemma 5.3.1 -- 5.7. Expansion formulas -- 6. The Unitary Inversion Operator -- 6.1. Result of the section -- 6.2. Inversion and Plancherel formula -- 6.3. The Hankel transform -- 6.4. Forward and backward light cones -- 7. Explicit Actions of the Whole Group on L2(C) -- 7.1. Bruhat decomposition of O(m + 1 -- 2) -- 7.2. Explicit action of the whole group -- 8. Appendix: Special Functions -- 8.1. Laguerre polynomials -- 8.2. Hermite polynomials -- 8.3. Gegenbauer polynomials -- 8.4. Spherical harmonics and Gegenbauer polynomials -- 8.5. Bessel functions -- References.

Classification des Series Discretes pour Certains Groupes Classiques p-Adiques Colette MEglin -- 1. Support Cuspidal des S eries Discr etes -- 2. Morphismes Associes aux Representations Cuspidales de G(n) et Points de Reductibilite des Induites de Cuspidales -- 3. Classification et Paquet de Langlands -- 4. Classification a la Langlands des Series Discretes de SO(2n + 1 -- F) -- 5. Le cas des Groupes Orthogonaux Impairs non Deployes -- References -- Some Algebras of Essentially Compact Distributions of a Reductive p-Adic Group Allen Moy and Marko Tadi c -- 1. Introduction -- 2. The Convolution Algebras H(G)b and U(G) -- 3. Some Properties of the Convolution Algebras H(G)b and U(G) -- 4. Some Explicit G-invariant Essentially Compact Distributions -- Acknowledgment -- References -- Annihilators of Generalized Verma Modules of the Scalar Type for Classical Lie Algebras Toshio Oshima -- 1. Introduction -- 2. Minimal Polynomials -- 3. Projection to the Cartan Subalgebra -- 4. Generalized Verma Modules -- 5. Integral Transforms on Generalized Flag Manifolds -- 6. Closure of Ideals -- References -- Branching to a Maximal Compact Subgroup David A. Vogan, Jr. -- Contents -- 1. General Introduction -- 2. Technical Introduction -- 3. Highest Weights for K -- 4. The R-Group of K and Irreducible Representations of the Large Cartan -- 5. Fundamental Series, Limits, and Continuations -- 6. Characters of Compact Tori -- 7. Split Tori and Representations of K -- 8. Parametrizing Extended Weights -- 9. Proof of Lemma 8.13 -- 10. Highest Weights for K and -Stable Parabolic Subalgebras -- 11. Standard Representations, Limits, and Continuations -- 12. More Constructions of Standard Representations -- 13. From Highest Weights to Discrete Final Limit Parameters -- 14. Algorithm for Projecting a Weight on the Dominant Weyl Chamber.

15. Making a List of Representations of K -- 16. G-Spherical Representations as Sums of Standard Representations -- References -- Small Semisimple Subalgebras of Semisimple Lie Algebras Jeb F. Willenbring and Gregg J. Zuckerman -- 1. Introduction -- 2. Invariant Theory -- 3. Representation Theory -- 4. A Proof of a Theorem in Penkov-Zuckerman -- 5. Example: G2 -- 6. Tables for Maximal Parabolic Subalgebras -- References.