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General


This course is part of the MAGIC core.

Description

Please see the syllabus.

Semester

Spring 2019 (Monday, January 21 to Friday, March 29)

Hours

  • Live lecture hours: 20
  • Recorded lecture hours: 0
  • Total advised study hours: 80

Timetable

  • Mon 11:05 - 11:55
  • Fri 10:05 - 10:55

Prerequisites

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

Syllabus

Representation Theory
Spring 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 finite dimensional representations over C. The main results are that such representations are completely reducible and completely determined by their characters. We will also see how characters are used to effectively calculate such decompositions. We will finish the course by studying two classes of examples.

Course Plan:
  • Review of linear algebra (complex inner product spaces, spectral theorem)
  • General linear group
  • (Complex) representations of groups
  • Maschke’s Theorem
  • Morphisms of representation, Schur’s Lemma
  • Orthogonality relations
  • Class functions, characters, and character tables
  • Regular representation
  • Representations of abelian groups
  • Representations of the symmetric group

Reference Texts:
  1. W. Fulton, J. Harris; Representation Theory - A First Course
  2. P. Etingof, O. Golberg, S. Hensel, T. Liu, A. Schwendner, D. Vaintrob, E. Yudovina; Introduction to representation theory
  3. J.-P. Serre; Linear representations of finite groups
  4. C. Curtis, I. Reiner; Methods of Representation Theory, John Wiley & Sons, New York 1981.
  5. I. M. Isaacs; Character Theory of Finite Groups, Academic Press, New York 1976.
  6. 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


Bibliography


Representations and Characters of GroupsG. James, M. Liebeck
Character Theory of Finite GroupsIsaacs
Methods of Representation Theory C. Curtis, I. Reiner
Introduction to representation theoryEtingof
Linear representations of finite groupsSerre


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Assessment



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Recorded Lectures


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