# MAS8709 : Representation theory

• Offered for Year: 2021/22
• Module Leader(s): Dr Martina Balagovic
• Owning School: Mathematics, Statistics and Physics
• Teaching Location: Newcastle City Campus
##### Semesters
 Semester 2 Credit Value: 10 ECTS Credits: 5

#### Aims

To introduce the basic ideas of studying groups through their representations as matrices, and to describe finite dimensional complex representations of finite groups.

Module Summary

The module presents the theory of finite dimensional complex representations of finite groups including the discussion of important classes of examples. Starting from the motivating question how a group can act linearly on a vector space, students will see an instance of a complete mathematical theory. While of major importance for the study of finite groups, this setup also forms a starting point for more general representation theory.

#### Outline Of Syllabus

Review of group theory, general linear group. Review of linear algebra. (Complex) representations of groups (subrepresentations, morphisms of representations). Maschke’s Theorem. Schur’s Lemma. Characters and orthogonality relations. Regular representation. Projection formulas. Representations of the symmetric group.

#### Teaching Methods

##### Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture201:0020:00Formal Lectures – Present in Person
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision Lectures – Present in Person
Scheduled Learning And Teaching ActivitiesLecture51:005:00Problem Classes – Synchronous On-Line
Guided Independent StudyIndependent study151:0015:00Completion of in course assessments
Guided Independent StudyIndependent study581:0058:00Preparation time for lectures, background reading, coursework review
Total100:00
##### Jointly Taught With
Code Title
MAS3709Representation theory
##### Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.

#### Assessment Methods

The format of resits will be determined by the Board of Examiners

##### Exams
Description Length Semester When Set Percentage Comment
Written Examination1202A80N/A
##### Exam Pairings
Module Code Module Title Semester Comment
MAS3709Representation theory2N/A
##### Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises2M10Coursework assignments
Prob solv exercises2M10Coursework assignment
##### Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The coursework assignments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.

In the event of on-campus examinations not being possible, an on-line alternative assessment will be used for written examination 1.