Representation theory I - finite groups
Summary
This is a standard course in representation theory of finite groups.
Content
This course is an introduction to representation theory. We start with basic notions and results in representation theory of associative algebras. The case of the representations of finite groups over C is treated in detail. We study the classical character theory with many examples. We introduce the notions of induction, restriction and tensor product of representations. In particular, we study the representations of symmetric groups over complex numbers.
Keywords
Representation, subrepresentation, irreducible representation, character, character tables, tensor product of representations, induced representation.
Learning Prerequisites
Required courses
Linear algebra
Recommended courses
Abstract algebra: groups
Learning Outcomes
By the end of the course, the student must be able to:
- Analyze representations of a finite group
- Identify irreducible representation, subrepresentation
- Compute character of a representation
- Construct an induced representation
- Analyze a tensor product of representations
Teaching methods
Lectures and problem sessions.
Assessment methods
One written homework (15% of the grade) and a written exam (85% of the grade).
Supervision
| Assistants | Yes |
| Forum | Yes |
Resources
Bibliography
P. Etingof et al., "Introduction to Representation Theory"
W. Fulton, J.Harris, "Representation Theory: A first course"
Ressources en bibliothèque
Notes/Handbook
Notes of the course will be available in PDF.
Moodle Link
Dans les plans d'études
- Semestre: Automne
- Forme de l'examen: Ecrit (session d'hiver)
- Matière examinée: Representation theory I - finite groups
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel