241054 Representations and Characters of finite Groups (S) (SoSe 2014)

Contents, comments: The main objective of this seminar is to discuss the basic concepts of representation theory and character theory of finite groups, investigate some properties of characters, construct character tables of some finite groups and apply character theory to the study of finite groups.

Modules, representations, Schur’s Lemma, semisimplicity, Maschke’s Theorem. Characters, orthogonal relations. Intergrity, Burnside p^aq^b Theorem. Tensor products, products of characters. Class functions, induction and restriction, M-groups, Mackey’s formula. TI-sets, Frobenius groups. Clifford Theory. Brauer’s Theorem. Modular representations. Possibly, representations of symmetric groups.

Requirements for participation, required level

Algebra I

Bibliography

Bibliography
1. Isaacs, I. Martin Character theory of finite groups, AMS Chelsea Publishing, Providence, RI, 2006. xii+310 pp. ISBN: 978-0-8218-4229-4; 0-8218-4229-3
2. James, Gordon; Liebeck, Martin, Representations and characters of groups. Second edition. Cambridge University Press, New York, 2001. viii+458 pp. ISBN: 0-521-00392-X
3. Huppert, Bertram, Character theory of finite groups, de Gruyter Expositions in Mathematics, 25. Walter de Gruyter & Co., Berlin, 1998. vi+618 pp. ISBN: 3-11-015421-8
4. Serre, Jean-Pierre, Linear representations of finite groups, Graduate Texts in Mathematics, Vol. 42. Springer-Verlag, New York-Heidelberg, 1977. x+170 pp. ISBN: 0-387-90190-6
5. Fulton, William; Harris, Joe, Representation theory, A first course. Graduate Texts in Mathematics, 129. Readings in Mathematics. Springer-Verlag, New York, 1991. xvi+551 pp. ISBN: 0-387-97527-6; 0-387-97495-4
6. James, Gordon; Kerber, Adalbert, The representation theory of the symmetric group. With a foreword by P. M. Cohn. With an introduction by Gilbert de B. Robinson. Encyclopedia of Mathematics and its Applications, 16. Addison-Wesley Publishing Co., Reading, Mass., 1981. xxviii+510 pp. ISBN: 0-201-13515-9