Representation theory for Lie groups and algebras
|Erasmus code / ISCED:||
|Course title:||Representation theory for Lie groups and algebras|
|Name in Polish:||Teoria reprezentacji grup i algebr Liego|
|Organizational unit:||Faculty of Mathematics, Informatics, and Mechanics|
(in Polish) Przedmioty obieralne na studiach drugiego stopnia na kierunku bioinformatyka
|ECTS credit allocation (and other scores):||
|Type of course:||
The basic concepts of the representation theory of Lie groups will be presented. Numerous specific interesting examples will be discussed in detail. If necessary, lectures may be held in English.
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
6. Representations of the general linear group, Young diagrams and
7. Root systems and classification of Lie groups.
8. Homogeneous spaces and related representations. Borel-Weil-Bott
Fulton, William; Harris, Joe - Representation theory. A first course.
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.
|Assessment methods and assessment criteria:||
Evaluation is based on results from
60% written exam
20% oral exam
Copyright by University of Warsaw.