Seminar: Lie algebras and representation theory

Wintersemester 2014/2015

Lecturer
Dr. Ana Peón-Nieto
INF 288, office 108
Website.
Email: apeonnieto [at] mathi.uni-heidelberg.de

Time and Location
Wednesdays 11 - 13 Room HS 4,

Description
After some introductory lectures on basic Lie theory, we will move on to the study of representations of simple Lie algebras, departing from particular examples towards a general framework. We will follow the book "Representation theory: a first course" by W. Fulton and J. Harris, from which the students are required to choose a chapter which they should present. I encourage you to look further into the subjects, though, so any reference can be used.

Evaluation
I will explain the basic prerequisites on Lie theory. The following meetings will be based on student presentations. The goal is to learn how to use representation theory, and for that one needs to...use them! So I will prepare one or two simple exercises for each lecture (from which the speaker is excused). The final mark is computed by 70%*(presentation mark)+30%*(exercises mark).

Prerequisites
Linear algebra. Some basic differential geometry can be useful. This course is suitable for bachelor/master students from mathematics and physics. The seminar will be taught in English.

Organization
Interested students should come to the organizational meeting on Wednesday 15.10.2014, HS 6 or send me an email and let me know what project you would like to carry out. There will be some lectures the first weeks covering the basics in Lie theory. I will be available during office hours to discuss the projects in more detail and help you during the preparation of your presentation.

Exercises: Sheet 1, Sheet 2 , Sheet 3, Sheet 4, Sheet 5.

Schedule

 Date Time Speaker Title Building Room 3.12.2014 11:15am Danilo Ciaffi Representations of sl(2,C) INF 288 HS4 10.12.2014 11:15am Benedetta Cavalli Representations of sl(n,C) 17.12.2014 11:15am Ingolf Bischer Representations of so(n,C) 28.01.2015 11:15am Simon Hirscher The adjoint representation 04.02.2015 11:15am Yannick Krifka Representations of compact groups

References
Fulton and Harris: Representation theory: a first course
Knapp: Lie groups beyond an introduction (for Lie theory)

last updated: 17th November 2014