Harmonic Analysis, Group Representations, Automorphic Forms and Invariant Theory : In Honor of Roger E Howe.

Harmonic Analysis, Group Representations, Automorphic Forms and Invariant Theory : In Honor of Roger E Howe.

This volume carries the same title as that of an international conference held at the National University of Singapore, 9-11 January 2006 on the occasion of Roger E. Howe's 60th birthday. Authored by leading members of the Lie theory community, these contributions, expanded from invited lecture...

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Bibliographic Details
Main Author: Li, Jian-Shu
Other Authors: Tan, Eng-Chye, Wallach, Nolan, Zhu, Chen-Bo
Format: eBook
Language:English
Published: Singapore : World Scientific Publishing Company, 2007.
Series:Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore.
Subjects:
Automorphic forms > Congresses.
Harmonic analysis > Congresses.
Representations of groups > Congresses.
Symmetry (Mathematics) > Congresses.
Automorphic forms
Harmonic analysis
Representations of groups
Symmetry (Mathematics)
Conference papers and proceedings
Online Access:Click for online access
Table of 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 Wallach1. 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 HarrisIntroduction; 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 D1.2. 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(2R); 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.

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