Representation Theory
A.Y. 2025/2026
Learning objectives
The aim of the course is to present the basic Ideas of Representation Theory for finite groups.
Expected learning outcomes
Knowledge of the basic ideas of Representation Theory for finite groups.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
Linear representations of finite groups:
irreducible representations, Schur's lemma and character theory; restriction, induction and Frobenius reciprocity; Artin's and Brauer's induction theorems; rationality questions.
Artin L-functions:
Galois theory and Artin representations; Kronecker-Weber theorem and Dirichlet L-functions; class field theory and Hecke L-functions; Artin L-functions and Artin's conjecture; modular forms and Artin L-functions.
irreducible representations, Schur's lemma and character theory; restriction, induction and Frobenius reciprocity; Artin's and Brauer's induction theorems; rationality questions.
Artin L-functions:
Galois theory and Artin representations; Kronecker-Weber theorem and Dirichlet L-functions; class field theory and Hecke L-functions; Artin L-functions and Artin's conjecture; modular forms and Artin L-functions.
Prerequisites for admission
Algebra 1-3. A basic understanding of Number Theory and Complex Analysis is recommended.
Teaching methods
Blackboard lectures.
Teaching Resources
Jean-Pierre Serre: Linear representations of finite groups.
W. Fulton, J. Harris: Representation Theory (A first course).
S. Lang: Algebraic Number Theory.
W. Fulton, J. Harris: Representation Theory (A first course).
S. Lang: Algebraic Number Theory.
Assessment methods and Criteria
The final examination consists of a written exam and an oral discussion, to be given in the same session. It is not allowed to use notes, books or calculators.
Professor(s)