58吃瓜

MT5871 Representation Theory

Academic year

2026 to 2027 Semester 1

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

The Scottish Credit Accumulation and Transfer (SCOTCAT) system allows credits gained in Scotland to be transferred between institutions. The number of credits associated with a module gives an indication of the amount of learning effort required by the learner. European Credit Transfer System (ECTS) credits are half the value of SCOTCAT credits.

SCQF level

SCQF level 11

The Scottish Credit and Qualifications Framework (SCQF) provides an indication of the complexity of award qualifications and associated learning and operates on an ascending numeric scale from Levels 1-12 with SCQF Level 10 equating to a Scottish undergraduate Honours degree.

Planned timetable

11.00 am Mon (weeks 2, 4, 7, 9, 11), Tue & Thu

This information is given as indicative. Timetable may change at short notice depending on room availability.

Module coordinator

Dr M Quick

This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module Staff

Dr Martyn Quick

This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module description

A common way to study groups, both historically and in modern research, is to consider the ways in which they act upon vector spaces. This module will describe the study of linear representations, bringing together ideas from group theory, ring theory and linear algebra. It will be shown how a linear representation can be decomposed into irreducible representations and how these can be determined using the structure of the group algebra. The module will introduce fundamental techniques to study linear representations, including the character of a representation and the character table of a group.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT3501 AND PASS MT3505 AND PASS MT4003

Assessment pattern

2-hour Written Examination = 100%

Re-assessment

Oral examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5 lectures (x 10 weeks), 1 tutorial (x 10 weeks)

Scheduled learning hours

35

The number of compulsory student:staff contact hours over the period of the module.

Guided independent study hours

115

The number of hours that students are expected to invest in independent study over the period of the module.

Intended learning outcomes

  • Demonstrate an understanding of the link between linear representations and modules for the group algebra.
  • Compute the character table of some finite groups, such as alternating groups and symmetric groups of small degree and cyclic groups.
  • State and use theorems concerning the decomposition of the group algebra and its modules, such as Schur鈥檚 Lemma, Maschke鈥檚 Theorem and the Wedderburn-Artin Theorem as it applies to group algebras.
  • Use representation theory to analyse given groups, for example using character theory to establish the existence of normal subgroups.
  • Use their knowledge to engage in creative problem-solving involving the above concepts.