This book adds to the great body of research that extends back to A. Weil and E. P. Wigner on the unitary representations of locally compact groups and their characters, i.e. the interplay between classical group theory and modern analysis. The groups studied here are the connected Lie groups of general type (not necessarily nilpotent or semisimple).
Final results reflect Kirillov's orbit method; in the case of groups that may be non-algebraic or non-type I, the method requires considerable sophistication. Methods used range from deep functional analysis (the theory of C∗-algebras, factors from F. J. Murray and J. von Neumann, and measure theory) to differential geometry (Lie groups and Hamiltonian actions).
This book presents for the first time a systematic and concise compilation of proofs previously dispersed throughout the literature. The result is an impressive example of the deepness of Pukánszky's work.
Readership: Graduate students and research mathematicians working in topological groups and Lie groups; theoretical physicists

nexusstc/Characters of connected Lie groups/75297423fae7a6e5e78d87b5b8203ea7.pdf

lgli/Characters of Connected Lie Groups.pdf

lgrsnf/Characters of Connected Lie Groups.pdf

zlib/Mathematics/Lajos Pukanszky/Characters of Connected Lie Groups_2344741.pdf

Lajos Pukánszky

Pukanszky, L.

Ziga Media, LLC

Mathematical surveys and monographs, no. 71, Providence, RI, ©1999

American Mathematical Society, Providence, RI, 1999

71 Mathematical Surveys and Monographs, 1999

United States, United States of America

September 1999

0

lg1176263

{"isbns":["082181088X","1619831511","9780821810880","9781619831513"],"last_page":128,"periodical":"71","publisher":"American Mathematical Society","series":"Mathematical Surveys and Monographs"}

Contents 8
Preface 10
Foreword 12
Introduction 14
Some notation used throughout the book 18
Chapter I. Unitary Representations of Locally Algebraic Groups 20
1.1. On a theorem of Chevalley 20
1.2. Locally algebraic groups 20
1.3. Proof of Main Lemma 27
1.4. Application to the regular representation of a connected Lie group 39
Chapter II. Representations of Elementary Groups 50
2.1. Special case: Extensions of free abelian groups 50
2.2. Proof of Main Proposition 58
2.3. Primitive ideals of class one 64
2.4. Surjectivity; first step 65
2.5. Surjectivity; second step 67
2.6. Proof of Lemma 4 69
2.7. Surjectivity; last step 71
2.8. Summary 72
Chapter III. Existence of Characters 74
3.1. Some subgroups of G 74
3.2. The orbits of J 82
3.3. Proof that J is surjective 89
3.4. Technical tools 93
3.5. Existence of normal representations with given kernels 105
3.6. The type I case 109
3.7. The non-type I case 109
3.8. Proof of principal result 117
3.9. The theorem of Poguntke 118
Chapter IV. Generalized Kirillov Theory 120
4.1. Preliminary facts 121
4.2. Construction of holomorphic representations 122
4.3. Extension of an irreducible representation 124
4.4. Computation of U[sub(π)] and K[sub(π)] 127
4.5. Holomorphically induced representations 131
4.6. Proof that ind is independent of the polarization 134
4.7. Condition for unitary equivalence 135
4.8. Regularized orbits 136
4.9. Generalized orbits 138
4.10. Auxiliary facts 140
4.11. Proof that J is surjective 142
4.12. Construction of a normal representation with kernel J 143
4.13. Type-one primitive ideals 144
References 146

Table of Contents
Unitary representations of locally algebraic groups
Unitary representations of elementary groups
Existence of characters
Generalized Kirillov theory
Bibliograph

2014-05-29