Representations of Reductive Groups, Avraham Aizenbud, Dmitry Gourevitch, David Kazhdan, Erez M. Lapid

Автор: Hall Brian
Название: Lie Groups, Lie Algebras, and Representations
ISBN: 3319134663 ISBN-13(EAN): 9783319134666
Издательство: Springer
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Цена: 50810.00 T
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Описание:

This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject.

In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including:

• a treatment of the Baker-Campbell-Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras
• motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C)
• an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras
• a self-contained construction of the representations of compact groups, independent of Lie-algebraic arguments

The second edition of Lie Groups, Lie Algebras, and Representations contains many substantial improvements and additions, among them: an entirely new part devoted to the structure and representation theory of compact Lie groups; a complete derivation of the main properties of root systems; the construction of finite-dimensional representations of semisimple Lie algebras has been elaborated; a treatment of universal enveloping algebras, including a proof of the Poincar -Birkhoff-Witt theorem and the existence of Verma modules; complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formula.

Review of the first edition

This is an excellent book. It deserves to, and undoubtedly will, become the standard text for early graduate courses in Lie group theory ... an important addition to the textbook literature ... it is highly recommended.

-- The Mathematical Gazette

Автор: Conrad
Название: Pseudo-reductive Groups
ISBN: 1107087236 ISBN-13(EAN): 9781107087231
Издательство: Cambridge Academ
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Цена: 119330.00 T
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Описание: This monograph provides a comprehensive treatment of the theory of pseudo-reductive groups and gives their classification in a usable form. This second edition has been revised and updated, with Chapter 9 being completely rewritten via the useful new notion of `minimal type` for pseudo-reductive groups.

Автор: Greco Michael
Название: Reductive Lie Groups
ISBN: 1632383993 ISBN-13(EAN): 9781632383990
Издательство: Неизвестно
Цена: 101920.00 T
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Автор: Peter Woit
Название: Quantum Theory, Groups and Representations
ISBN: 3319646109 ISBN-13(EAN): 9783319646107
Издательство: Springer
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Цена: 74530.00 T
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Описание: The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject.

Автор: Matthew J. Emerton
Название: Locally Analytic Vectors in Representations of Locally $p$-adic Analytic Groups
ISBN: 0821875620 ISBN-13(EAN): 9780821875629
Издательство: Mare Nostrum (Eurospan)
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Цена: 74850.00 T
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Описание: Provides the foundations for the locally analytic representation theory that is required in three of the author`s other papers on this topic. In the course of writing those papers the author found it useful to adopt a particular point of view on locally analytic representation theory: namely, regarding a locally analytic representation as being the inductive limit of its subspaces of analytic vectors.