Representations of Lie Groups
Compact Lie groups, Peter–Weyl, and highest-weight theory.
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 · 2015Lie Groups, Lie Algebras, and Representationshall-2015
- textbook · primary · 2004Representation Theory: A First Coursefulton-2004, harris-2004
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