Representation Theory

News

The course will be held in English. First lecture on 21/10.

Topics

The aim of this course is to learn what Representation Theory is and how to use it. The main reference will be Fulton-Harris' book (see below).

Even though most of the contents will be defined from scratch, knowledge of complex and differential geometry is recommended.

Tentative topics of this course are

• Representations of Finite Groups
• Representations of SL_n and GL_n and their Lie Algebras
• Representations of Semisimple Lie Algebras
• Borel-Weil-Bott-Schmid Theorem
• Homogeneous varieties

Literature

• W. Fulton, J. Harris. 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.
• J.M. Landsberg. Tensors: geometry and applications. Graduate Studies in Mathematics, 128. American Mathematical Society, Providence, RI, 2012. xx+439 pp. ISBN: 978-0-8218-6907-9.

Other literature will be added here before or during the lectures.

Workload

• 3 hours lectures, 1 hour exercise session per week
• 45h hours total time for lectures
• 15h hours total time for excercises

Lectures

The lectures take place on:

Tuesday 14:00-15:30 in SR 7, Building E2 4 and

Wednesday 12:30-14 in SR 8, Building E2 4

Exam

A quick written exam with correction/discussion and an oral part.

Exercises

Exercise sessions should take place every second Tuesday and last 90 min, as a usual lecture. These are intented to offer the students advice and solutions about the exercises that are given from time to time during the lectures. First exercise session: 4/11. f

Contacts