Seminar/Proseminar on the representation theory of the symmetric group, Winter Semester 2019

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Organiser: Victoria Hoskins.

Time and location: Monday 14:00-16:00 in SR130, Arnimallee 3.

Prerequisites: Linear algebra.

Organisation: This is a seminar in which the participants give the talks; for guidelines on preparing your talk see the seminar plan below. Please send me an email () if you would like to reserve one of the talks, or if you have any questions.

First meeting: Monday 14.10.19, 14:00 -16:00.


A representation of a group is an action of the group on a vector space; that is, for each element in the group, we have an automorphism of the vector space, and their compositions are compatible with the group multiplication. In this seminar we will focus on the representation theory of finite groups, and in particular the symmetric group. Many prominent mathematicians have studied the representation theory of the symmetric group, such as Frobenius, Schur and Young. The representation theory of the symmetric group also has strong connections to combinatorics, geometry and topology, as well as applications to other branches of mathematics, such as mathematical physics. Every representation is built out of irreducible representations and the main aim will be to describe these irreducible representations for the symmetric group combinatorially using partitions and so-called Young diagrams. This forms the foundations for studying the representation theory of matrix groups like the general linear group (and, more generally, Lie groups).

Seminar plan: A detailed plan of the talks is available here.

Main reference : B. E. Sagan, The symmetric group: representations, combinatorial algorithms, and symmetric functions, second ed., Graduate texts in mathematics, vol. 203, Springer, 1991.

Schedule of the talks:

♠ 14.10.2019 // Talk 1: Algebraic foundations - Victoria Hoskins

♠ 28.10.2019 // Talk 2: The symmetric group and its conjugacy classes - Charlotte Weschke

♠ 04.11.2019 // Talk 3 : Group representations and the group algebra - Rebecca Sattler

♠ 11.11.2019 // Talk 4: Reducibility and Maschke’s Theorem - Joshua Röber

♠ 18.11.2019 // Talk 5: Schur’s Lemma and the commutant algebra - Stephanie Hoffmann

♠ 25.11.2019 // Talk 6: Tensor products of matrix representations and the commutant algebra - Martin Günther

♠ 02.12.2019 // Talk 7: Group characters and the character table - Alessia Maria Barbanti

♠ 09.12.2019 // Talk 8: Orthogonality relations for characters - Fynn Birkemeyer

♠ 16.12.2019 // Talk 9: Consequences of the orthogonality relations - Norbert Pape