MATH-334 / 5 crédits

Enseignant:

Langue: Anglais

Remark: pas donné en 2021-22


Summary

Study the basics of representation theory of groups and associative algebras.

Content

Keywords

Linear representation, subrepresentation, quotient, semisimple representation, character of a representation, associative algebra, representation of a finite group, character table, orthogonality relations, induced representation, restricted representation, symmetric group, Young diagram. 

Learning Prerequisites

Required courses

Linear algebra or Advanced Linear algebra; Group theory

Recommended courses

Lie algebras, Coxeter groups

Learning Outcomes

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

  • Apply concepts and ideas of the course
  • Reason rigorously using the notions of the course
  • Choose an appropriate method to solve problems
  • Identify the concepts relevant to each problem
  • Apply concepts to solve problems similar to the questions in problem sets
  • Solve new problems using the ideas of the course
  • Implement appropriate methods to study and construct representations of groups and algebras

Teaching methods

Lectures and exercise sessions

Assessment methods

One take-home written assignment (15% of the grade) 

Written exam (85% of the grade) 

 

Supervision

Office hours No
Assistants Yes
Forum No

Resources

Bibliography

1. P. Etingof, O. Goldberg, S. Hensel, T. Liu, A. Schwendner, D. Vaintrob, E. Yudovina, "Introduction to Representation Theory".   Student Mathematical Library Volume: 59; 2011. ISBN: 978-0-8218-5351-1

2. Fulton, William, and Joe Harris. Representation Theory: A First Course. Graduate texts in mathematics. Vol. 129. New York, NY: Springer, 1991. ISBN: 9780387974958.

Ressources en bibliothèque

Dans les plans d'études

  • Semestre: Printemps
  • Forme de l'examen: Ecrit (session d'été)
  • Matière examinée: Representation theory
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 2 Heure(s) hebdo x 14 semaines

Semaine de référence

 LuMaMeJeVe
8-9     
9-10     
10-11     
11-12     
12-13     
13-14     
14-15     
15-16     
16-17     
17-18     
18-19     
19-20     
20-21     
21-22