Dewey Class 
512.55 
512.482 
Title 
Representation Theory ([EBook]) : A First Course / by William Fulton, Joe Harris. 
Author 
Fulton, William. , 1939 
Added Personal Name 
Harris, Joe. , 1951 author. 
Other name(s) 
SpringerLink (Online service) 
Publication 
New York, NY : Springer , 2004. 
Physical Details 
XV, 551 pages : online resource. 
Series 
Graduate Texts in Mathematics, Readings in Mathematics 00725285 ; ; 129 
ISBN 
9781461209799 
Summary Note 
The primary goal of these lectures is to introduce a beginner to the finite dimensional representations of Lie groups and Lie algebras. Since this goal is shared by quite a few other books, we should explain in this Preface how our approach differs, although the potential reader can probably see this better by a quick browse through the book. Representation theory is simple to define: it is the study of the ways in which a given group may act on vector spaces. It is almost certainly unique, however, among such clearly delineated subjects, in the breadth of its interest to mathematicians. This is not surprising: group actions are ubiquitous in 20th century mathematics, and where the object on which a group acts is not a vector space, we have learned to replace it by one that is {e. g. , a cohomology group, tangent space, etc. }. As a consequence, many mathematicians other than specialists in the field {or even those who think they might want to be} come in contact with the subject in various ways. It is for such people that this text is designed. To put it another way, we intend this as a book for beginners to learn from and not as a reference. This idea essentially determines the choice of material covered here. As simple as is the definition of representation theory given above, it fragments considerably when we try to get more specific.: 
Contents note 
I: Finite Groups  1. Representations of Finite Groups  2. Characters  3. Examples; Induced Representations; Group Algebras; Real Representations  4. Representations of 15 and Other Exceptional Lie Algebras  23. Complex Lie Groups; Characters  24. Weyl Character Formula  25. More Character Formulas  26. Real Lie Algebras and Lie Groups  Appendices  A. On Symmetric Functions  §A.1: Basic Symmetric Polynomials and Relations among Them  §A.2: Proofs of the Determinantal Identities  §A.3: Other Determinantal Identities  B. On Multilinear Algebra  §B.1: Tensor Products  §B.2: Exterior and Symmetric Powers  §B.3: Duals and Contractions  C. On Semisimplicity  §C.1: The Killing Form and Caftan’s Criterion  §C.2: Complete Reducibility and the Jordan Decomposition  §C.3: On Derivations  D. Cartan Subalgebras  §D.1: The Existence of Cartan Subalgebras  §D.2: On the Structure of Semisimple Lie Algebras  §D.3: The Conjugacy of Cartan Subalgebras  §D.4: On the Weyl Group  E. Ado’s and Levi’s Theorems  §E.1: Levi’s Theorem  §E.2: Ado’s Theorem ^F. Invariant Theory for the Classical Groups  §F.1: The Polynomial Invariants  §F.2: Applications to Symplectic and Orthogonal Groups  §F.3: Proof of Capelli’s Identity  Hints, Answers, and References  Index of Symbols 
System details note 
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users) 
Internet Site 
http://dx.doi.org/10.1007/9781461209799 
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