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Representation theory for Lie groups and algebras

General data

Course ID: 1000-1M07TR
Erasmus code / ISCED: 11.104 Kod klasyfikacyjny przedmiotu składa się z trzech do pięciu cyfr, przy czym trzy pierwsze oznaczają klasyfikację dziedziny wg. Listy kodów dziedzin obowiązującej w programie Socrates/Erasmus, czwarta (dotąd na ogół 0) – ewentualne uszczegółowienie informacji o dyscyplinie, piąta – stopień zaawansowania przedmiotu ustalony na podstawie roku studiów, dla którego przedmiot jest przeznaczony. / (0541) Mathematics The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
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:
ECTS credit allocation (and other scores): (not available) Basic information on ECTS credits allocation principles:
  • the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS;
  • the student’s weekly hourly workload is 45 h;
  • 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes;
  • weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS;
  • work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load.

view allocation of credits
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



Basic source:

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

20% tutorials

60% written exam

20% oral exam

This course is not currently offered.
Course descriptions are protected by copyright.
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