Table of Contents

Compact Lie Groups.- Representations.- HarmoniC Analysis.- Lie Algebras.- Abelian Lie Subgroups and Structure.- Roots and Associated Structures.- Highest Weight Theory.

Reviews

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)