Harmonic analysis, group representations, automorphic forms, and invariant theory : in honor of Roger E. Howe / editors, Jian-Shu Li.

Format:

Book

Conference/Event

Author/Creator:

International Conference on Harmonic Analysis, Group Representations, Automorphic Forms, and Invariant Theory, Corporate Author.

Contributor:

Howe, Roger.

Li, Jian-Shu.

Conference Name:

International Conference on Harmonic Analysis, Group Representations, Automorphic Forms and Invariant Theory (2006 : National University of Singapore)

International Conference on Harmonic Analysis, Group Representations, Automorphic Forms, and Invariant Theory

Series:

Lecture notes series (National University of Singapore. Institute for Mathematical Sciences) ; v. 12.

Lecture notes series / Institute for Mathematical Sciences, National University of Singapore, 1793-0758 ; v. 12

Language:

English

Subjects (All):

Symmetry (Mathematics)--Congresses.

Symmetry (Mathematics).

Harmonic analysis--Congresses.

Harmonic analysis.

Representations of groups--Congresses.

Representations of groups.

Automorphic forms--Congresses.

Automorphic forms.

Physical Description:

1 online resource (448 p.)

Edition:

1st ed.

Place of Publication:

Singapore ; Hackensack, N.J. : World Scientific, 2007.

Language Note:

English

Summary:

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 lectures given at the conference, are a fitting tribute to the originality, depth and influence of Howe's mathematical work. The range and diversity of the topics will appeal to a broad audience of research mathematicians and graduate students interested in symmetry and its profound applications. <i>Sample Ch

Contents:

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

5.3. Proof of Theorem 5.1.1 (Case Re t > 0)

Notes:

"To honor Howe's exceptional achievements ... an International Conference on Harmonic Analysis, Group Representations, Automorphic Forms, and Invariant Theory was held at the National University of Singapore (NUS) from January 9-11, 2006, on the occasion of his 60th birthday."--P. ix.

Includes bibliographical references.

ISBN:

9786611911591

9781281911599

1281911593

9789812770790

9812770798

OCLC:

879023562