Representation of General Lie Groups and General Lie Algebras

  • Masahito HayashiEmail author


Based on root systems, this chapter deals with representations of a Lie group via those of the corresponding Lie algebra. This chapter discusses a non-compact Lie group as well as a compact Lie group. To discuss both, we focus on the relation between a (real) Lie algebra and a complex Lie algebra. Since representations of a non-compact group are very complicated, this chapter treats only a part of its representations that are related to quantum theory. As such special representation has analogies with representations of a compact Lie group, they can be more easily understood than the general case. Since this chapter is composed of very advanced topics and such sections are labeled with *, the reader can omit this chapter in the first time.

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Graduate School of MathematicsNagoya UniversityNagoyaJapan

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