Blending algebra, analysis, and topology, the study of compact
Lie groups is one of the most beautiful areas of mathematics and a
key stepping stone to the theory of general Lie groups. Assuming no
prior knowledge of Lie groups, this book covers the structure and
representation theory of compact Lie groups. Coverage includes the
construction of the Spin groups, Schur Orthogonality, the
Peter-Weyl Theorem, the Plancherel Theorem, the Maximal Torus
Theorem, the Commutator Theorem, the Weyl Integration and Character
Formulas, the Highest Weight Classification, and the Borel-Weil
Theorem. The book develops the necessary Lie algebra theory with a
streamlined approach focusing on linear Lie groups.
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