Department of Mathematics

INDIAN INSTITUTE OF SCIENCE

MA 320: Representation theory of compact Lie groups

Credits: 3:0

Prerequisite courses: MA 223

Lie groups, Lie algebras, matrix groups , representations, Schur’s orthogonality relations, Peter-Weyl theorem, structure of compact semisimple Lie groups, maximal tori, roots and rootspaces, classification of fundamental systems Weyl group, Highest weight theorem, Weyl integration formula, Weyl’s character formula.

Suggested books and references:

1. V. S. Varadarajan, Lie groups, Lie algebras and their representations, Sringer 1984.
2. A. C. Hall, Lie groups, Lie algebras and representations, Springer 2003.
3. Barry Simon, Representations of finite and compact groups, AMS 1996.
4. A. W. Knapp, Representation theory of semismiple lie groups. An overview based on examples, Princeton university press 2002.

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