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MARC 21

Representation Theory: A First Course
Tag	Description
020	$a9781461209799
082	$a512.55
082	$a512.482
099	$aOnline resource: Springer
100	$aFulton, William.$d1939-
245	$aRepresentation Theory$h[EBook]$bA First Course$cby William Fulton, Joe Harris.
260	$aNew York, NY$bSpringer$c2004.
300	$aXV, 551 pages$bonline resource.
336	$atext
338	$aonline resource
440	$aGraduate Texts in Mathematics, Readings in Mathematics,$x0072-5285 ;$v129
505	$aI: 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
520	$aThe 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.
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
700	$aHarris, Joe.$d1951-$eauthor.
710	$aSpringerLink (Online service)
830	$aGraduate Texts in Mathematics, Readings in Mathematics,$v129
856	$uhttp://dx.doi.org/10.1007/978-1-4612-0979-9