Representations of Lie Groups

Compact Lie groups, Peter–Weyl, and highest-weight theory.


field tier

Representations of Lie Groups. Compact Lie groups, Peter–Weyl, and highest-weight theory.

Foundations and canonical references

The standard treatments of representations of lie groups approach the subject from complementary angles. Hall, Lie Groups, Lie Algebras, and Representations (2015) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Fulton, Representation Theory: A First Course (2004) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.

Open methodological questions for representations of lie groups include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.

Prerequisites

Sources

  • textbook · primary · 2015
    Lie Groups, Lie Algebras, and Representations
    hall-2015
  • textbook · primary · 2004
    Representation Theory: A First Course
    fulton-2004, harris-2004

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