Representation Theory II - Lie groups and algebras

MATH-429 / 5 credits

Teacher: Negut Andrei

Language: English

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

Learning Prerequisites

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

Resources

Bibliography

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

D. Bump, "Lie Groups"

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

Ressources en bibliothèque

Moodle Link

In the programs

  • Semester: Spring
  • Exam form: Written (summer session)
  • Subject examined: Representation Theory II - Lie groups and algebras
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Spring
  • Exam form: Written (summer session)
  • Subject examined: Representation Theory II - Lie groups and algebras
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional
  • Semester: Spring
  • Exam form: Written (summer session)
  • Subject examined: Representation Theory II - Lie groups and algebras
  • 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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