Characters of connected lie groups / Lajos Pukánszky.

Format:

Book

Author/Creator:

Pukanszky, L., author.

Series:

Mathematical surveys and monographs ; no. 71.

Mathematical surveys and monographs, 0076-5376 ; volume 71

Language:

English

Subjects (All):

Lie groups.

Characters of groups.

Representations of Lie groups.

Physical Description:

1 online resource (149 p.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [1999]

Language Note:

English

Summary:

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 Pukanszky's work.

Contents:

""Contents""; ""Preface""; ""Foreword""; ""Introduction""; ""Some notation used throughout the book""; ""Chapter I. Unitary Representations of Locally Algebraic Groups""; ""1.1. On a theorem of Chevalley""; ""1.2. Locally algebraic groups""; ""1.3. Proof of Main Lemma""; ""1.4. Application to the regular representation of a connected Lie group""; ""Chapter II. Representations of Elementary Groups""; ""2.1. Special case: Extensions of free abelian groups""; ""2.2. Proof of Main Proposition""; ""2.3. Primitive ideals of class one""; ""2.4. Surjectivity; first step""; ""2.5. Surjectivity

second step""""2.6. Proof of Lemma 4""; ""2.7. Surjectivity; last step""; ""2.8. Summary""; ""Chapter III. Existence of Characters""; ""3.1. Some subgroups of G""; ""3.2. The orbits of J""; ""3.3. Proof that J is surjective""; ""3.4. Technical tools""; ""3.5. Existence of normal representations with given kernels""; ""3.6. The type I case""; ""3.7. The non-type I case""; ""3.8. Proof of principal result""; ""3.9. The theorem of Poguntke""; ""Chapter IV. Generalized Kirillov Theory""; ""4.1. Preliminary facts""; ""4.2. Construction of holomorphic representations""

""4.3. Extension of an irreducible representation""""4.4. Computation of...""; ""4.5. Holomorphically induced representations""; ""4.6. Proof that ind is independent of the polarization""; ""4.7. Condition for unitary equivalence""; ""4.8. Regularized orbits""; ""4.9. Generalized orbits""; ""4.10. Auxiliary facts""; ""4.11. Proof that J is surjective""; ""4.12. Construction of a normal representation with kernel J""; ""4.13. Type-one primitive ideals""; ""References""

Notes:

Description based upon print version of record.

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-1298-5