Theory of representations 1

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Basic knowledge about representations of groups, with emphasize given to finite groups.

Requirements:

basic mathematical analysis and linear algebra course (01MAN, 01MAA2-01MAA4, 01LAL, 01LAA2), algebra course (01ALGE)

Syllabus of lectures:

1. The notion of group and its representation. Irreducible representations. Schur's lemma.

2. Direct sum and direct product of representations.

3. Representation characters, orthogonality, Burnside theorem.

4. Character tables.

5. Representations of permutation group.

6. Induced representations, normal subgroups, projective representations.

Syllabus of tutorials:

Study Objective:

Knowledge: basic notions and procedures in representations of finite groups, basic outlook in construction methods.

Skills: explicit construction of representations and character tables of given finite group, analysis of given representation (irreducibility)

Study materials:

Key references:

1. B. Steinberg: Representation Theory of Finite Groups: An Introductory Approach, Springer, 2011

2. J. P. Serre: Linear Representations of Finite Groups, Springer, 2012

Recommended references:

3. B. Simon: Representations of Finite and Compact Groups, AMS, 1996

4. A. Wilson: Modular Representation Theory of Finite Groups, Scitus Academics LLC, 2016

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Aplikovaná algebra a analýza (compulsory course in the program)