This course is the continuation of "Advanced topics in Algebra A1".
A group representation on a vector space is a group homomorphism from a group to the group of invertible linear transformations on a vector space.
The aim of this course is to explain fundamental facts in the representation theory of finite groups;
in particular, we explain tensor product representations, induced representations, and the relationship between restriction and induction of group representations.
The goal of this course is to understand how the regular representation of a finite group (on its group algebra) decomposes into irreducibles ones.
tensor product representation, regular representation, induced representation, Frobenius reciprocity
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Standard lecture course.
Course schedule | Required learning | |
---|---|---|
Class 1 | Regular representation | Details will be provided during each class session. |
Class 2 | Irreducible decomposition of the regular representation | Details will be provided during each class session. |
Class 3 | Tensor product representations | Details will be provided during each class session. |
Class 4 | Representation matrices of tensor product representations | Details will be provided during each class session. |
Class 5 | Induced representations | Details will be provided during each class session. |
Class 6 | Representation matrices of induced representations | Details will be provided during each class session. |
Class 7 | Relationship between restriction and induction of representations | Details will be provided during each class session. |
Class 8 | Frobenius Reciprocity | Details will be provided during each class session. |
To enhance effective learning, students are encouraged to spend approximately 30 minutes preparing for class and another 30 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
None.
Bruce E. Sagan, The Symmetric Group, GTM, No. 203, Springer.
Based on evaluation of assignments. Details will be announced during each class session.
None