**
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)