Compact Lie Groups: 235 (Graduate Texts in Mathematics) - Tapa dura

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From the reviews:

"Groups serve to parameterize the symmetries of mathematical objects and the ways symmetries combine. ... offers students willing to take a few things on faith a vital vista on a subject they may wish to pursue at the graduate level. Summing Up: Recommended. Upper-division undergraduates through professionals." (D. V. Feldman, CHOICE, Vol. v4 (3), November, 2007)

"The representation theory of compact groups is an old and venerable subject. The problems and solutions are now well understood and serve as a guide for the more advanced parts of the representation theory. ... The present one is intended as a textbook within the reach of a good undergraduate student. ... The reading should be pleasant both for students and for teachers preparing a course on the subject." (David A. Renard, Mathematical Reviews, Issue 2008 a)

“This book offers an introduction to the theories of compact Lie groups and of Lie algebras, which is organized in an unusual way. ... For the ambitious reader many exercises are provided.” (A. Cap, Monatshefte für Mathematik, Vol. 158 (2), October, 2009)

Reseña del editor

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.