MA 320: Representation theory of compact Lie groups
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 :
V. S. Varadarajan, Lie groups, Lie algebras and their representations
A. C. Hall, Lie groups, Lie algebras and representations
Barry Simon, Representations of finite and compact groups
A. W. Knapp, Representation theory of semismiple lie groups. An overview based on examples
,Princeton university press 2002.
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