Representation theory for Lie groups and algebras
General data
Course ID: | 1000-1M07TR |
Erasmus code / ISCED: |
11.104
|
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 |
Course groups: |
(in Polish) Przedmioty obieralne na studiach drugiego stopnia na kierunku bioinformatyka |
Course homepage: | http://duch.mimuw.edu.pl/~aweber/zadania/Lie |
ECTS credit allocation (and other scores): |
(not available)
|
Language: | English |
Type of course: | elective monographs |
Short description: |
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. |
Full description: |
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. |
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. |
Assessment methods and assessment criteria: |
Evaluation is based on results from 20% tutorials 60% written exam 20% oral exam |
Copyright by University of Warsaw.