| Book Description | This book is intended as an introduction to the theory of Lie groups and their representations at the advanced undergraduate or beginning graduate level. It covers the essentials of the subject starting from basic undergraduate mathematics. The correspondence between linear Lie groups and Lie algebras is developed in its local and global aspects. The classical groups are analysed in detail, first with elementary matrix methods, then with the help of the structural tools typical of the theory of semisimple groups, such as Cartan subgroups, roots, weights, and reflections. The fundamental groups of the classical groups are worked out as an application of these methods. Manifolds are introduced when need |
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