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# Representation Theory of Classical Groups - MAT00047M

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• Department: Mathematics
• Module co-ordinator: Prof. Maxim Nazarov
• Credit value: 10 credits
• Credit level: M
• Academic year of delivery: 2019-20
• See module specification for other years: 2018-19

• None

• None

## Module will run

Occurrence Teaching cycle
A Spring Term 2019-20

## Module aims

• To learn general properties of representations and characters of finite groups.

• To learn classical combinatorics related to the symmetric group.

• To learn explicit construction of irreducible representations of the symmetric group.

## Module learning outcomes

At the end of the module students should know:

• Representation of a group by linear transformations of a vector space.

• Characters of representations of finite groups over the complex field.

• Irreducible representations of the symmetric group over the complex field.

• The Robinson-Schensted-Knuth algorithm and its inverse.

## Module content

[Pre-requisite knowledge for MSc students: first course on Linear Algebra, first course on Group Theory; a basic knowledge of rings and fields would be desirable.]

The module content will include the following principal topics:

• General properties of representations of finite groups.

• General properties of characters of finite groups.

• Conjugacy classes in the symmetric group and combinatorics of Young diagrams.

• Irreducible representations of the symmetric group over the complex field.

• Young symmetrizers and the regular representation of the symmetric group.

• The Robinson-Schensted-Knuth algorithm and its inverse.

## Assessment

Task Length % of module mark
24 hour open exam
Representation Theory of Classical Groups
N/A 100

None

### Reassessment

Task Length % of module mark
24 hour open exam
Representation Theory of Classical Groups
N/A 100

## Module feedback

Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy.

G D James, Representation and Characters of Groups (2nd edition), CUP, 2005.

B E Sagan, The symmetric group: representations, combinatorial algorithms and symmetric functions, Wadsworth and Brooks/Cole, 1991.

The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.

## Coronavirus (COVID-19): changes to courses

The 2020/21 academic year will start in September. We aim to deliver as much face-to-face teaching as we can, supported by high quality online alternatives where we must.

Find details of the measures we're planning to protect our community.