Representation Theory of Semisimple Groups: An Overview Based onExamples

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.

About the author

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.

Summary

Offers a survey of representation theory of semisimple Lie groups. Suitable for both graduate students and researchers, this book states the theorems precisely, and gives many illustrative examples or classes of examples. It includes for the reader a useful 300-item bibliography and an extensive section of notes.

Additional text

"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

Product details

• Authors: Anthony W. Knapp, A.W. Knapp, Anthony W. Stein, Anthony Knapp, Knapp Anthony W.
• Assisted by: John N. Mather (Editor), Phillip Griffiths (Editor)
• Publisher: Princeton University Press
• Content: Book
• Product form: Paperback / Softback
• Publication date: 24.10.2001
• Subject: Education and learning > Teaching preparation > Vocational needs
• EAN: 9780691090894
• ISBN: 978-0-691-09089-4
• Pages: 800
• Dimensions (packing): 15.6 x 23.5 x 4.4 cm
• Series: Princeton Landmarks in Mathema; Princeton Mathematical Series; Princeton Landmarks in Mathematics and Physics
• Subjects: Algebra, MATHEMATICS / Algebra / General, Theorem, category theory, Hilbert space, vector bundle, representation theory, Lie algebra, holomorphic function, mathematical induction, Tensor Algebra, Hermitian matrix, Eigenfunction, automorphism, associative algebra, Eigenvalues and Eigenvectors, Variable (mathematics), Sign (mathematics), Set (mathematics), Diagram (category theory), Summation, Subgroup, Dimension (vector space), Degenerate bilinear form, General linear group, Infinitesimal character, Algebra homomorphism, Distribution (mathematics), Projection (linear algebra), Invertible matrix, Symplectic group, Semisimple Lie algebra, Topological space, Special linear group, Discrete series representation, Admissible representation, Hyperbolic function, Norm (mathematics), Invariant subspace, Fourier inversion theorem, Irreducible representation, Cartan Subalgebra, Group homomorphism, Heine–Borel theorem, Automorphic form, Conjugate transpose, Explicit formulae (L-function), Weyl group, Weyl's theorem, Topological group, Cartan subgroup, Identity (mathematics), Complexification (Lie group), Representation of a Lie group, Bounded operator, Matrix coefficient, Continuous function (set theory), Jacobian matrix and determinant, Matrix group, Nilpotent Lie algebra, Zorn's lemma, Solvable Lie algebra, Classification theorem, Special unitary group, Unitary representation, Bounded set (topological vector space), Characterization (mathematics), Unitary matrix, Weight (representation theory), Complex conjugate representation, Schwartz space, Locally integrable function