Representation theory for Lie groups and algebras 1000-1M07TR
1. Classical complex and real matrix groups. Detailed study of
SU(2), SL(2,C), SO(3) and their representations.
2. Quaternions and Clifford algebras.
3. Elements of general theory of Lie groups. Lie Algebras.
4. Basic theory of compact Lie groups and linear reductive groups.
Maximal compact subgroups, complexification.
5. Representations of tori, weights and representations of
classical groups.
6. Representations of the general linear group, Young diagrams and
polynomial functors.
7. Root systems and classification of Lie groups.
8. Homogeneous spaces and related representations. Borel-Weil-Bott
theorem.
Type of course
Assessment criteria
Evaluation is based on results from
20% tutorials
60% written exam
20% oral exam
Bibliography
Basic source:
Fulton, William; Harris, Joe - Representation theory. A first course.
Moreover:
Adams, J.F. - Lectures on Lie groups.
Carter, Roger; Segal, Graeme; Macdonald, Ian - Lectures on Lie groups and Lie algebras. London Mathematical Society Student Texts, 32.
Knapp, Anthony W. - Representation theory of semisimple groups. An overview based on examples.
Additional information
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