MATH-429 / 5 crédits

Enseignant: Negut Andrei

Langue: Anglais

## Summary

This is a standard course on Lie groups, Lie algebras and their representations.

## Content

This is a second semester course in representation theory. We will study Lie groups and Lie algebras, with particular emphasis on algebraic aspects, and with the guiding examples of the classical groups in mind. We will also classify representations of Lie groups and Lie algebras, and discuss their character theory.

## Keywords

Lie groups, Lie algebras, classical groups, representations, character formulas

## Required courses

MATH-211 Group theory

MATH-314 Representation theory I - finite groups

## Recommended courses

MATH-213 Differential geometry

## Learning Outcomes

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

• Formulate the main concepts and theorems defined in the course
• Theorize the role of Lie groups and Lie algebras in the theory
• Compute the characters of certain Lie group / Lie algebra representations

## Teaching methods

Lectures and problem sessions

## Expected student activities

Students are expected to attend all lectures and participate in all problem sessions.

## Assessment methods

One written homework (15% of the grade) and a written exam (85% of the grade).

## Supervision

 Office hours No Assistants Yes Forum Yes

## Bibliography

W. Fulton, J.Harris, "Representation Theory: A first course"

D. Bump, "Lie Groups"

A. Baker, "Matrix Groups: An Introdudion to Lie Group Theory"

## Dans les plans d'études

• Semestre: Printemps
• Forme de l'examen: Ecrit (session d'été)
• Matière examinée: Representation Theory II - Lie groups and algebras
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Type: optionnel
• Semestre: Printemps
• Forme de l'examen: Ecrit (session d'été)
• Matière examinée: Representation Theory II - Lie groups and algebras
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Type: optionnel
• Semestre: Printemps
• Forme de l'examen: Ecrit (session d'été)
• Matière examinée: Representation Theory II - Lie groups and algebras
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Type: optionnel

## Cours connexes

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