Real Reductive Grups I

Science & Math

Wallach, Nolan R.

Mathematics

Academic Press

Real Reductive Groups I is an introduction to the representation theory of real reductive groups. It is based on courses that the author has given at Rutgers for the past 15 years. It also had its genesis in an attempt of the author to complete a manuscript of the lectures that he gave at the CBMS regional conference at The University of North Carolina at Chapel Hill in June of 1981. This book comprises 10 chapters and begins with some background material as an introduction. The following chapters then discuss elementary representation theory; real reductive groups; the basic theory of (g, K)-modules; the asymptotic behavior of matrix coefficients; The Langlands Classification; a construction of the fundamental series; cusp forms on G; character theory; and unitary representations and (g, K)-cohomology. This book will be of interest to mathematicians and statisticians.

Real Reductive Groups I, Vol. 132 (Pure and Applied Mathematics) (Volume 132)

Symmetry is a key ingredient in many mathematical, physical, and biological theories. Using representation theory and invariant theory to analyze the symmetries that arise from group actions, and with strong emphasis on the geometry and basic theory of Lie groups and Lie algebras, Symmetry, Representations, and Invariants is a significant reworking of an earlier highly-acclaimed work by the authors. The result is a comprehensive introduction to Lie theory, representation theory, invariant theory, and algebraic groups, in a new presentation that is more accessible to students and includes a broader range of applications. The philosophy of the earlier book is retained, i.e., presenting the principal theorems of representation theory for the classical matrix groups as motivation for the general theory of reductive groups. The wealth of examples and discussion prepares the reader for the complete arguments now given in the general case. Key Features of Symmetry, Representations, and Invariants: (1) Early chapters suitable for honors undergraduate or beginning graduate courses, requiring only linear algebra, basic abstract algebra, and advanced calculus; (2) Applications to geometry (curvature tensors), topology (Jones polynomial via symmetry), and combinatorics (symmetric group and Young tableaux); (3) Self-contained chapters, appendices, comprehensive bibliography; (4) More than 350 exercises (most with detailed hints for solutions) further explore main concepts; (5) Serves as an excellent main text for a one-year course in Lie group theory; (6) Benefits physicists as well as mathematicians as a reference work.

Symmetry, Representations, and Invariants (Graduate Texts in Mathematics, 255)

Goodman, Roe

Springer

This book derives from author Nolan R. Wallach's notes for a course on symplectic geometry and Fourier analysis, which he delivered at Rutgers University in 1975 for an audience of graduate students in mathematics and their professors. The monograph is geared toward readers who have taken a basic course in differential manifolds and elementary functional analysis. The first chapters cover certain geometric preliminaries, advancing to discussions of symplectic geometry and the application of its concepts to the action of a Lie group on a symplectic manifold. Subsequent chapters address Fourier analysis, the metaplectic representation, and quantization. A final chapter on the Kirillov theory applies the ideas of the previous chapters to homogeneous symplectic manifolds of nilpotent Lie groups. The book concludes with an Appendix on Quantum Mechanics by Robert Hermann.

Symplectic Geometry and Fourier Analysis: Second Edition (Dover Books on Mathematics)

Dover Publications

This book is suitable for advanced undergraduate and graduate students in mathematics with a strong background in linear algebra and advanced calculus. Early chapters develop representation theory of compact Lie groups with applications to topology, geometry, and analysis, including the Peter-Weyl theorem, the theorem of the highest weight, the character theory, invariant differential operators on homogeneous vector bundles, and Bott's index theorem for such operators. Later chapters study the structure of representation theory and analysis of non-compact semi-simple Lie groups, including the principal series, intertwining operators, asymptotics of matrix coefficients, and an important special case of the Plancherel theorem. Teachers will find this volume useful as either a main text or a supplement to standard one-year courses in Lie groups and Lie algebras. The treatment advances from fairly simple topics to more complex subjects, and exercises appear at the end of each chapter. Eight helpful Appendixes develop aspects of differential geometry, Lie theory, and functional analysis employed in the main text.

Harmonic Analysis on Homogeneous Spaces: Second Edition (Dover Books on Mathematics)

More than half a century has passed since Weyl's "The Classical Groups" gave a unified picture of invariant theory that has retained its importance in mathematics and physics to the present day. This book presents an updated version of this theory together with many of the important recent developments. As a text for beginners, this book provides an introduction to the structure and finite-dimensional representation theory of the complex classical groups that requires only an abstract algebra course as a prerequisite. It makes abundant use of examples and exercises to explain concepts such as root systems, Weyl groups and highest weight theory. The more advanced reader will find an introduction to the structure and representations of complex reductive algebraic groups and their compact real forms. This book will also serve as a reference for the main results on tensor and polynomial invariants and the finite-dimensional representation theory of the classical groups. It will appeal to researchers in mathematics, statistics, physics and chemistry whose work involves symmetry groups, representation theory, invariant theory and algebraic group theory.

Representations and Invariants of the Classical Groups (Encyclopedia of Mathematics and its Applications, Series Number 68)

Reference

Encyclopedias & Subject Guides

Cambridge University Press

More than half a century has passed since Weyl's "The Classical Groups" gave a unified picture of invariant theory that has retained its importance in mathematics and physics to the present day. This book presents an updated version of this theory together with many of the important recent developments. As a text for beginners, this book provides an introduction to the structure and finite-dimensional representation theory of the complex classical groups that requires only an abstract algebra course as a prerequisite. It makes abundant use of examples and exercises to explain concepts such as root systems, Weyl groups and highest weight theory. The more advanced reader will find an introduction to the structure and representations of complex reductive algebraic groups and their compact real forms. This book will also serve as a reference for the main results on tensor and polynomial invariants and the finite-dimensional representation theory of the classical groups. It will appeal to researchers in mathematics, statistics, physics and chemistry whose work involves symmetry groups, representation theory, invariant theory and algebraic group theory.

Representations and Invariants of the Classical Groups (Encyclopedia of Mathematics and its Applications, Volume 68)

The description for this book, Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups. (AM-94), Volume 94, will be forthcoming.

Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups. (AM-94), Volume 94 (Annals of Mathematics Studies, 94)

Borel, Armand

Princeton University Press

The Description for this book, Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups. (AM-94), will be forthcoming.

It has been nearly twenty years since the first edition of this work. In the intervening years, there has been immense progress in the use of homological algebra to construct admissible representations and in the study of arithmetic groups. This second edition is a corrected and expanded version of the original, which was an important catalyst in the expansion of the field. Besides the fundamental material on cohomology and discrete subgroups present in the first edition, this edition also contains expositions of some of the most important developments of the last two decades.

Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups (Mathematical Surveys & Monographs)

Amer Mathematical Society

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Books by Wallach, Nolan R.

See the best price to sell, buy, or rent books by Wallach, Nolan R.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Real Reductive Grups I

Real Reductive Groups I, Vol. 132 (Pure and Applied Mathematics) (Volume 132)

Symmetry, Representations, and Invariants (Graduate Texts in Mathematics, 255)

Symplectic Geometry and Fourier Analysis: Second Edition (Dover Books on Mathematics)

Harmonic Analysis on Homogeneous Spaces: Second Edition (Dover Books on Mathematics)

Representations and Invariants of the Classical Groups (Encyclopedia of Mathematics and its Applications, Series Number 68)

Representations and Invariants of the Classical Groups (Encyclopedia of Mathematics and its Applications, Volume 68)

Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups. (AM-94), Volume 94 (Annals of Mathematics Studies, 94)

Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups. (AM-94), Volume 94 (Annals of Mathematics Studies, 94)

Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups (Mathematical Surveys & Monographs)