Topic outline

  • General

    Course description

    Groups and their representations form the mathematical description of symmetries. This course introduces you to representation theory, with particular emphasis on Lie groups and their Lie algebras which account for continuous symmetries. Mathematical applications of the theory range from combinatorics to geometry and topology. Lie groups of importance to physics include the group of coordinate transformations of spacetime in special relativity, and the group of gauge transformations in theories of particle physics.

    Contents
    Representations of finite groups.
    Lie groups and their Lie algebras.
    Representations of semisimple Lie algebras.


    Time
    2021-2022 Period III (6 weeks)
    • Lectures, 2 x 2h / week: Mondays 10-12 (hall U5?) and Wednesdays 10-12 (hall D)
    • Exercise sessions 1 x 2h / week: Wednesdays 14-16 (hall Y229a)

    Prerequisites

    Abstract algebra (MS-C1081)
    Differential and integral calculus (MS-A02XX)
    Matrix algebra (MS-A00XX)


    Grading
    The course grade is determined by a score consisting of
    • up to 24 points from the exam (4 problems worth 6 points each)
    • up to 6 bonus points from solutions to problems

    Exam
    The exam will be held on:
    • Wednesday, April 13 at ?? (lecture hall ??).
    The retake exam is on:
    • Thursday, June 2 at ?? (lecture hall ??).

    You are allowed to bring to the exam a handwritten memory aid sheet. The memory aid sheet must be of size A4 with text only on one side, and it must contain your name and student number in the upper right corner. You don’t need to return your memory aid sheet. The exam consists of 4 problems, each worth 6 points.


    Exercises
    There are weekly problem sets, posted under the "Assignments" tab on this page.


    Literature
    For lecture notes and schedule see the Lectures section.

    The official textbook is
    • W. Fulton & J. Harris "Representation theory: A first course", Graduate Texts in Mathematics. Springer, 2004.

    Other relevant textbooks and material are listed in the Materials section.