Representation theory II - Lie algebras

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 semisimple Lie algebras, and discuss their characters.

Keywords

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

Learning Prerequisites

Required courses

MATH-211 Group theory

MATH-314 Representation theory I - finite groups

MATH-322 Differential geometry II - smooth manifolds

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, read all the lecture notes, 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

Resources

Moodle Link

Dans les plans d'études

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

Semaine de référence

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