Representation Theory: A First Course: 129 (Graduate Texts in Mathematics, 129)

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 variou