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General


This course is part of the MAGIC core.

Description

Please see the syllabus.

Semester

Spring 2017 (Monday, January 23 to Friday, March 31)

Timetable

  • Wed 11:05 - 11:55
  • Thu 12:05 - 12:55

Prerequisites

A course on group theory and a good background in linear algebra.

Syllabus

Representation Theory
Fall Term
Lecturer: Kay Magaard
Outline of course: This course is an introduction to the representation theory of finite groups. We will develop the basic theory of ordinary representations and their characters. Along the way we will compute the charcter tables of particular classes of groups. We will also examine how structural information of a group can be obtained from its character table. For large parts we will mostly follow Isaacs book; see the references below.
Course Plan:
  • (Week 1) Basic definitions, the group algebra, Wedderburn theory.
  • (Week 2) Characters and the Orthogonality relations.
  • (Week 3) Examples of character tables.
  • (Week 4) Integrality, Burnside's paqb Theorem.
  • (Weeks 5) Products of characters, the representations ring.
  • (Week 6) Involutions and the Brauer-Fowler Thereom
  • (Week 7) Induced Characters, Frobenius reciprocity, permutation characters.
  • (Weeks 8 and 9) Clifford's theorem and consequences.
  • (Weeks 9 and 10) Forbenius' theorem and related results.

Reference Texts:
  1. C. Curtis, I. Reiner; Methods of Representation Theory, John Wiley & Sons, New York 1981.
  2. I. M. Isaacs; Character Theory of Finite Groups, Academic Press, New York 1976.
  3. G. James, M. Liebeck; Representations and Characters of Groups, 2nd Edition, Cambridge University Press, 2001.

Lecturer


Kay Magaard
Email k.magaard@bham.ac.uk
Phone
vcard


Students


Photo of Mashaer Alsaeedi
Mashaer Alsaeedi
(Birmingham)
Photo of Turki Alsuraiheed
Turki Alsuraiheed
(Sheffield)
Photo of Stuart Bond
Stuart Bond
(Sussex)
Photo of Ho Yiu Chung
Ho Yiu Chung
(Southampton)
Photo of Padraig Condon
Padraig Condon
(Birmingham)
Photo of Alberto ESPUNY DIAZ
Alberto ESPUNY DIAZ
(Birmingham)
Photo of Samuel Ford
Samuel Ford
(York)
Photo of Richard Hatton
Richard Hatton
(Nottingham)
Photo of Vijay Joshi
Vijay Joshi
(Birmingham)
Photo of Ulla Karhumäki
Ulla Karhumäki
(Manchester)
Photo of Bianca Loda
Bianca Loda
(*Ext_Assessed)
Photo of James Macpherson
James Macpherson
(East Anglia)
Photo of Rosario Mennuni
Rosario Mennuni
(Leeds)
Photo of William Norledge
William Norledge
(Newcastle)
Photo of Andrea Pachera
Andrea Pachera
(Birmingham)
Photo of Sam Povall
Sam Povall
(Liverpool)
Photo of Jack Saunders
Jack Saunders
(Birmingham)
Photo of Kathryn Spalding
Kathryn Spalding
(Loughborough)
Photo of Anna Szumowicz
Anna Szumowicz
(Durham)
Photo of Matty Van Son
Matty Van Son
(Liverpool)
Photo of George Witty
George Witty
(East Anglia)
Photo of Yiru Ye
Yiru Ye
(Loughborough)
Photo of Di Zhang
Di Zhang
(Sheffield)


Bibliography


Representations and Characters of GroupsG. James, M. Liebeck
Character Theory of Finite GroupsIsaacs
Methods of Representation Theory C. Curtis, I. Reiner


Note:

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Assessment



The assessment for this course will be via a single take-home paper in April with 2 weeks to complete and submit online. There will be three questions worth a total of 60 marks. The pass mark is 30/60.

Final

Files:Exam paper
Released: Monday 24 April 2017 (63.4 days ago)
Deadline: Sunday 7 May 2017 (49.4 days ago)


Files


Files marked L are intended to be displayed on the main screen during lectures.

Week(s)File
1-15Notes2017.pdf


Recorded Lectures


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