Coursebooks 2017-2018

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Representation theory of semisimple Lie algebras

MATH-492

Lecturer(s) :

Testerman Donna

Language:

English

Summary

We will estbalish the major results in the representation theory of semisimple Lie algebras over the field of complex numbers, and that of the related algebraic groups.

Content

Highest weight theory

Universal enveloping algebra

Construction of irreducible representations

Weyl's degree formula

Freudenthal's formula.

 

If time permits, construction of Chevalley groups and simple algebraic groups.

Learning Prerequisites

Required courses

Theorie des Groupes, Anneaux et corps, Algebres de Lie semisimples

Important concepts to start the course

The classificaiton of complex semisimple Lie algebras. Root systems.

Teaching methods

Lectures

Expected student activities

Exercises, extra reading, presentation of exercises.

Assessment methods

Final written exam

Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.

Supervision

Office hours Yes
Assistants Yes

Resources

Bibliography

James Humphreys : Introduction to Lie algebras and Representation Theory.

 

Bourbaki, Lie algebras and Lie groups, Chapters 1 - 3.

In the programs

Reference week

 MoTuWeThFr
8-9     
9-10     
10-11     
11-12     
12-13     
13-14   BC02 
14-15    
15-16   BC02 
16-17    
17-18     
18-19     
19-20     
20-21     
21-22     
 
      Lecture
      Exercise, TP
      Project, other

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  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German