Module MATH4241: REPRESENTATION THEORY IV

Department: Mathematical Sciences

MATH4241: REPRESENTATION THEORY IV

Prerequisites

• Mathematics modules to the value of 100 credits in Years 2 and 3, with at least 40 credits at Level 3 and including Algebra II (MATH2581).

Corequisites

• None.

Excluded Combination of Modules

• Representation Theory III (MATH3371).

Aims

• To develop and illustrate representation theory for finite groups and Lie groups.

Content

• Representations of finite groups.
• Character theory.
• Modules over group algebra.
• Lie groups and Lie algebras and their representations.
• Representations of SL(2,C), SU(2), SO(3).
• Reading material on a topic related to: Representations of the symmetric group, representations over finite fields.

Learning Outcomes

• By the end of the module students will: be able to solve novel and/or complex problems in Representation Theory.
• have a systematic and coherent understanding of theoretical mathematics in the field of Representation Theory.
• have acquired a coherent body of knowledge of these subjects demonstrated through one or more of the following topic areas: Representations of finite groups.
• Character tables.
• Induced representations, Frobenius reciprocity.
• Representations of abelian groups.
• Lie groups and algebras, exponential map.
• Examples of representations of Lie groups and algebras.

• In addition students will have highly specialised and advanced mathematical skills in the following areas: Abstract Reasoning.
• Students will have an advanced understanding in one of the following areas: Representations of the symmetric group, representations over finite fields.

• Students will have developed independent learning of an advanced topic.

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

• Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
• Subject material assigned for independent study develops the ability to acquire knowledge and understanding without dependence on lectures.
• Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
• Formatively assessed assignments provide practice in the application of logic and high level of rigour as well as feedback for the students and the lecturer on students' progress.
• The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

Eight written assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University