This book offers a systematic treatment--the first in book form--of the development and use of cohomological induction to construct unitary representations. George Mackey introduced induction in 1950 as a real analysis construction for passing from a unitary representation of a closed subgroup of a locally compact group to a unitary representation of the whole group. Later a parallel construction using complex analysis and its associated co-homology theories grew up as a result of work by Borel, Weil, Harish-Chandra, Bott, Langlands, Kostant, and Schmid. Cohomological induction, introduced...
This book offers a systematic treatment--the first in book form--of the development and use of cohomological induction to construct unitary represe...
This book starts with the elementary theory of Lie groups of matrices and arrives at the definition, elementary properties, and first applications of cohomological induction, which is a recently discovered algebraic construction of group representations. Along the way it develops the computational techniques that are so important in handling Lie groups. The book is based on a one-semester course given at the State University of New York, Stony Brook in fall, 1986 to an audience having little or no background in Lie groups but interested in seeing connections among algebra, geometry, and...
This book starts with the elementary theory of Lie groups of matrices and arrives at the definition, elementary properties, and first applications ...
An elliptic curve is a particular kind of cubic equation in two variables whose projective solutions form a group. Modular forms are analytic functions in the upper half plane with certain transformation laws and growth properties. The two subjects--elliptic curves and modular forms--come together in Eichler-Shimura theory, which constructs elliptic curves out of modular forms of a special kind. The converse, that all rational elliptic curves arise this way, is called the Taniyama-Weil Conjecture and is known to imply Fermat's Last Theorem.
Elliptic curves and the modeular forms...
An elliptic curve is a particular kind of cubic equation in two variables whose projective solutions form a group. Modular forms are analytic funct...
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.
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 s...
Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. The presentation includes blocks of problems that introduce additional topics and applications to science and engineering to guide further study. Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems.
Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or appl...
Basic Real Analysis systematically develops those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. Along with a companion volume Advanced Real Analysis (available separately or together as a Set via the Related Links nearby), these works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics.
Key topics and features of Basic Real Analysis
* Early chapters treat...
Basic Real Analysis systematically develops those concepts and tools in real analysis that are vital to every mathematician, whether pure ...
From reviews of the first edition: "The important feature of the present book is that it starts from the beginning (with only a very modest knowledge assumed) and covers all important topics... The book is very carefully organized and] ends with 20 pages of useful historic comments. Such a comprehensive and carefully written treatment of fundamentals of the theory will certainly be a basic reference and text book in the future." -- Newsletter of the EMS "This is a fundamental book and none, beginner or expert, could afford to ignore it. Some results are really difficult to be found in other...
From reviews of the first edition: "The important feature of the present book is that it starts from the beginning (with only a very modest knowledge ...
Advanced Real Analysis systematically develops those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. Along with a companion volume Basic Real Analysis (available separately or together as a Set via the Related Links nearby), these works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics.
Key topics and features of Advanced Real Analysis
* Develops Fourier...
Advanced Real Analysis systematically develops those concepts and tools in real analysis that are vital to every mathematician, whether pu...
