Representation theory of finite groups

MATH-314 / 5 credits

Teacher: Rizzoli Aluna

Language: English

Summary

Group representation theory studies the actions of groups on vector spaces. This allows the use of linear algebra to study certain group theoretical questions. In this course the groups in question will be finite and the vector spaces finite dimensional.

Content

  • Group representations, Maschke's Theorem
  • Group algebras, representations of algebras and modules, Artin-Wedderburn's theorem
  • Characters, Orthogonality relations
  • Constructing representations : tensor products, induced representations, Frobenius reciprocity

Keywords

representation, group, algebra, module, character

Learning Prerequisites

Required courses

Linear algebra, Anneaux et corps

Recommended courses

Théorie des groupes, Rings and modules

Important concepts to start the course

Linear algebra

Learning Outcomes

By the end of the course, the student must be able to:

  • Apply theorems to concrete examples
  • Quote results from the course
  • Prove certain results from the course

Transversal skills

  • Assess one's own level of skill acquisition, and plan their on-going learning goals.
  • Demonstrate the capacity for critical thinking

Teaching methods

Lectures and exercises

Assessment methods

Written exam

Supervision

Office hours Yes
Assistants Yes
Forum No

Resources

Virtual desktop infrastructure (VDI)

No

Bibliography

 

  • Representations and Characters of groups, G. D. James and M. W. Liebeck
  • Linear Representations of Finite Groups, J.-P. Serre
  • Character Theory of Finite Groups, I. M. Isaacs
  • Representation Theory: A First Course, W. Fulton and J. Harris

Références suggérées par la bibliothèque

Moodle Link

In the programs

  • Semester: Spring
  • Exam form: Written (summer session)
  • Subject examined: Representation theory of finite groups
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional

Reference week

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