Representation Theory: A First Course (Google eBook)

Front Cover
Springer Science & Business Media, 1991 - Mathematics - 551 pages
3 Reviews
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.
  

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Contents

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Copyright

Common terms and phrases

Popular passages

Page 528 - Let g be a Lie algebra. g is semisimple if and only if its Killing form is nondegenerate.
Page viii - Mumford, from whom we learned much of what we know about the subject, and whose ideas are very much in evidence in this book.
Page 8 - G-linear for every p if (and only if) g is in the center Z(G) of G. In...
Page 541 - The Weyl group is generated by the reflections in the simple roots, ie^ SB = $B0.

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About the author (1991)

Fulton is president of Solimar Research Group in Ventura, California.

Benedict Gross" is the Leverett Professor of Mathematics and Dean of Harvard College.

"Joe Harris" is the Higgins Professor of Mathematics and Chair of the Mathematics Department at Harvard.

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