Representation Theory II - Lie groups and algebras
Summary
This is a standard course on Lie groups, Lie algebras and their representations.
Content
This is a second semester course in representation theory. We will study Lie groups and Lie algebras, with particular emphasis on algebraic aspects, and with the guiding examples of the classical groups in mind. We will also classify representations of Lie groups and Lie algebras, and discuss their character theory.
Keywords
Lie groups, Lie algebras, classical groups, representations, character formulas
Learning Prerequisites
Required courses
MATH-211 Group theory
MATH-314 Representation theory I - finite groups
Recommended courses
MATH-213 Differential geometry
Learning Outcomes
By the end of the course, the student must be able to:
- Formulate the main concepts and theorems defined in the course
- Theorize the role of Lie groups and Lie algebras in the theory
- Compute the characters of certain Lie group / Lie algebra representations
Teaching methods
Lectures and problem sessions
Expected student activities
Students are expected to attend all lectures and participate in all problem sessions.
Assessment methods
One written homework (15% of the grade) and a written exam (85% of the grade).
Supervision
| Office hours | No |
| Assistants | Yes |
| Forum | Yes |
Resources
Bibliography
W. Fulton, J.Harris, "Representation Theory: A first course"
D. Bump, "Lie Groups"
A. Baker, "Matrix Groups: An Introdudion to Lie Group Theory"
Ressources en bibliothèque
- Introduction to Smooth Manifolds / Lee
- Lie groups, beyond an introduction / Knapp
- Matrix Groups / Baker
- Introduction to the Theory of Lie Groups / Godement
- Lie Groups / Bump
Moodle Link
In the programs
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Representation Theory II - Lie groups and algebras
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Representation Theory II - Lie groups and algebras
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Representation Theory II - Lie groups and algebras
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
Reference week
| Mo | Tu | We | Th | Fr | |
| 8-9 | |||||
| 9-10 | |||||
| 10-11 | |||||
| 11-12 | |||||
| 12-13 | |||||
| 13-14 | |||||
| 14-15 | |||||
| 15-16 | |||||
| 16-17 | |||||
| 17-18 | |||||
| 18-19 | |||||
| 19-20 | |||||
| 20-21 | |||||
| 21-22 |
Légendes:
Lecture
Exercise, TP
Project, other