Book
Licensed
Unlicensed
Requires Authentication
Representation Theory of Semisimple Groups
An Overview Based on Examples
-
Anthony W. Knapp
Language:
English
Published/Copyright:
1986
About this book
In this classic work, Anthony W. Knapp offers a survey of representation theory of semisimple Lie groups in a way that reflects the spirit of the subject and corresponds to the natural learning process. This book is a model of exposition and an invaluable resource for both graduate students and researchers. Although theorems are always stated precisely, many illustrative examples or classes of examples are given. To support this unique approach, the author includes for the reader a useful 300-item bibliography and an extensive section of notes.
Author / Editor information
Anthony W. Knapp is Emeritus Professor of Mathematics, State University of New York at Stony Brook. The author of numerous books, he is the former editor of the Notices of the American Mathematical Society.
Reviews
"Each [theme] is developed carefully and thoroughly, with beautifully worked examples and proofs that reflect long experience in teaching and research. . . . This result is delightful: a readable text that loses almost none of its value as a reference work."---David A. Vogan Jr., Bulletin of the American Mathematical Society
"Anthony Knapp has written a marvelous book. . . . Written with accuracy, style, and a genuine desire to communicate the materials. . . . This is one of the finest books I have ever had the pleasure to read, and I recommend it in the strongest possible terms to anyone wishing to appreciate the intricate beauty and technical difficulty of representation theory of semisimple Lie groups."---R. J. Plymen, Bulletin of the London Mathematical Society
"Winner of the 1997 Leroy P. Steele Prize, American Mathematics Society"
Topics
-
Download PDFPublicly Available
Frontmatter
i -
Download PDFPublicly Available
Contents
vii -
Requires Authentication UnlicensedLicensed
Preface to the Princeton Landmarks in Mathematics Edition
xiii -
Requires Authentication UnlicensedLicensed
Preface
xv -
Requires Authentication UnlicensedLicensed
Acknowledgments
xix -
Requires Authentication UnlicensedLicensed
Chapter I. Scope of the Theory
1 -
Requires Authentication UnlicensedLicensed
Chapter II. Representations of SU(2), SL(2, ℝ) and SL(2, ℂ)
28 -
Requires Authentication UnlicensedLicensed
Chapter III. C∞ Vectors and the Universal Enveloping Algebra
46 -
Requires Authentication UnlicensedLicensed
Chapter IV. Representations of Compact Lie Groups
60 -
Requires Authentication UnlicensedLicensed
Chapter V. Structure Theory for Noncompact Groups
113 -
Requires Authentication UnlicensedLicensed
Chapter VI. Holomorphic Discrete Series
150 -
Requires Authentication UnlicensedLicensed
Chapter VII. Induced Representations
167 -
Requires Authentication UnlicensedLicensed
Chapter VIII. Admissible Representations
203 -
Requires Authentication UnlicensedLicensed
Chapter IX. Construction of Discrete Series
281 -
Requires Authentication UnlicensedLicensed
Chapter X. Global Characters
333 -
Requires Authentication UnlicensedLicensed
Chapter XI. Introduction to Plancherel Formula
385 -
Requires Authentication UnlicensedLicensed
Chapter XII. Exhaustion of Discrete Series
426 -
Requires Authentication UnlicensedLicensed
Chapter XIII. Plancherel Formula
482 -
Requires Authentication UnlicensedLicensed
Chapter XIV. Irreducible Tempered Representations
515 -
Requires Authentication UnlicensedLicensed
Chapter XV. Minimal K Types
626 -
Requires Authentication UnlicensedLicensed
Chapter XVI. Unitary Representations
650 -
Requires Authentication UnlicensedLicensed
Appendix A. Elementary Theory of Lie Groups
667 -
Requires Authentication UnlicensedLicensed
Appendix B. Regular Singular Points of Partial Differential Equations
685 -
Requires Authentication UnlicensedLicensed
Appendix C. Roots and Restricted Roots for Classical Groups
713 -
Requires Authentication UnlicensedLicensed
Notes
719 -
Requires Authentication UnlicensedLicensed
References
747 -
Requires Authentication UnlicensedLicensed
Index of Notation
763 -
Requires Authentication UnlicensedLicensed
Index
767
Publishing information
Pages and Images/Illustrations in book
eBook published on:
June 2, 2016
eBook ISBN:
9781400883974
Edition:
With a New preface by the author
Pages and Images/Illustrations in book
Main content:
800
eBook ISBN:
9781400883974
Keywords for this book
Theorem; Lie algebra; Dimension (vector space); Complexification (Lie group); Group homomorphism; Semisimple Lie algebra; Cartan subgroup; Matrix coefficient; Locally integrable function; Diagram (category theory); Invertible matrix; Representation theory; Special linear group; Solvable Lie algebra; Bounded set (topological vector space); Nilpotent Lie algebra; Classification theorem; Projection (linear algebra); Norm (mathematics); Subgroup; Zorn's lemma; Algebra homomorphism; Weyl's theorem; Representation of a Lie group; Discrete series representation; Topological group; Continuous function (set theory); General linear group; Automorphic form; Characterization (mathematics); Distribution (mathematics); Matrix group; Identity (mathematics); Tensor algebra; Mathematical induction; Set (mathematics); Fourier inversion theorem; Associative algebra; Holomorphic function; Category theory; Summation; Invariant subspace; Eigenfunction; Unitary representation; Variable (mathematics); Automorphism; Jacobian matrix and determinant; Weight (representation theory); Hyperbolic function; Weyl group; Vector bundle; Special unitary group; Infinitesimal character; Explicit formulae (L-function); Heine–Borel theorem; Admissible representation; Unitary matrix; Cartan subalgebra; Irreducible representation; Conjugate transpose; Complex conjugate representation; Hilbert space; Topological space; Bounded operator; Degenerate bilinear form; Symplectic group; Schwartz space; Sign (mathematics); Eigenvalues and eigenvectors; Hermitian matrix
Audience(s) for this book
College/higher education;Professional and scholarly;
