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General


This course is part of the MAGIC core.

Description

Please see the syllabus.

Semester

Spring 2018 (Monday, January 22 to Friday, March 16; Monday, April 23 to Friday, May 4)

Timetable

  • Mon 16:05 - 16:55
  • Thu 12:05 - 12:55

Prerequisites

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

Syllabus

Representation Theory
Fall Term
Lecturer: Martina Balagovic
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


Martina Balagovic
Email Martina.Balagovic@newcastle.ac.uk
Phone
Photo of Martina Balagovic
Profile: Research interests: algebra, representation theory, quantum groups, quantum affine algebras, Kac-Moody algebras, double affine Hecke algebras and their degenerations, quantum symmetric pairs, Lie superalgebras, diagram algebras


Students


Photo of Nataliya Balabanova
Nataliya Balabanova
(Manchester)


Bibliography


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


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