Representation
Theory (Winter Semester 2014/15)
The course is addressed to Master students or Phase I BMS
Students.
Since the course is registered as a BMS course, it will be hold
in English (unless audience prefers German or Spanish language )
The contents of the course:
1. Representations of
finite groups
- Irreducibility and G-homorphisms (Schur's Lemma)
- Tensor, dual and induced representations
- Permutation representations
- Examples: Representation symmetric and alternating groups
2. Character theory
- Characters and class functions
- Character tables
- Reciprocity formulae
3. Representations of the symmetric group
- Irreducible representations and Young Diagrams
- Frobenius formula
4. Schur Functors
5. The group algebra
6. Induced representations
- Mackey´s irreducibility criterion
- Examples of induced representations
I will follow mostly the book of Harris-Fulton "Representation
Theory, a first course" (GTM 129, Springer)
and J.-P. Serre´s "Linear Representations of Finite
Groups"
( GTM 42, Springer ) . Eventually I will use
the Fulton's book "Young Tableaux" (LMS Student Texts 35)
The prerequisites are the courses of Linear Algebra and
Algebra.
For the moment there is no exercises session but I will leave
exercises every week to
work them out.
Exercises:
Sheet 1 (21.04)
Sheet
2 (03.05)
Sheet 3 (14.05)
Sheet 4 (27.05)
Sheet 5 (06.06)
Sheet
6 (25.06)
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