#### Summer 2022 - V4A3 Representation Theory I

(Introduction to the structure and representation theory of semisimple Lie algebras)

**Announcements:**

*The Einsicht (exam review: where you may review your marked exam) will be held on Thursday, September 22 at 12:30-13:30 in the Hausdorff Room of the Mathematical Institute on Endenicher Allee 60. *

**Old Announcements:**

*The Einsicht (exam review: where you may review your marked exam) will be held on Monday, July 25 at 12pm noon until 1pm in the Hausdorff Room of the Mathematical Institute on Endenicher Allee 60. *

*The exam will be on Wednesday 20.07.2022. It will begin at 9am sharp and last until 11am. It will be held in the Großer Hörsaal and Kleiner Hörsaal at Wegeler Str. 10.*

*There will be no lecture on Wednesday, May 18 due to Dies Academicus.*

**Instructor:** Prof. Dr. Catharina Stroppel

**Assistant:** Dr. Jacob Matherne

**Course content:** In this course, we will give an introduction to semisimple Lie
algebras. This will involve the basic notions and their classification. In particular, we will cover their representation theory.

**Lectures:**

Wednesdays 10–12 and Fridays 8–10 in the Kleiner Hörsaal at Wegeler Str. 10.

The lectures are planned to be held in person at the location above.

*The first lecture is on April 6.*

**Tutorials:**

The tutorials are planned to be held in person at the MI in Seminar Room 0.007.

Tutors and tutorial times:

- Monday 8–10: Bárbara Muniz
- Monday 10–12: Liao Wang
- Thursday 10–12: Jan Thomm
- Thursday 12–14: Zbigniew Wojciechowski

*The first tutorial will take place in the second week of the semester (April 11–15).*

*The distribution of the tutorial groups can now be found in the Sciebo folder, inside the folder "Material from tutorial".*

**Exercise sheets:**

Sheet | Due date | Comments |
---|---|---|

Live tutorial sheet | Not to submit | |

Exercise sheet 1 | Wednesday, April 13 at 10:15am | |

Exercise sheet 2 | Wednesday, April 20 at 10:15am | |

Exercise sheet 3 | Wednesday, April 27 at 10:15am | |

Exercise sheet 4 | Wednesday, May 4 at 10:15am | |

Exercise sheet 5 | Wednesday, May 11 at 10:15am | |

Exercise sheet 6 | Friday, May 20 at 8:15am | |

Exercise sheet 7 | Wednesday, May 25 at 10:15am | Updated to correct an issue with Problem 5. Please see the Sciebo announcement. |

Exercise sheet 8 | Wednesday, June 1 at 10:15am | |

Exercise sheet 9 | Wednesday, June 15 at 10:15am | |

Exercise sheet 10 | Wednesday, June 22 at 10:15am | |

Exercise sheet 11 | Wednesday, June 29 at 10:15am | |

Exercise sheet 12 | Wednesday, July 6 at 10:15am |

**Exam:**

- The first examination timeslot will be on Wednesday 20.07.2022 at 9–11 in the Großer Hörsaal and Kleiner Hörsaal at Wegeler Str. 10.
- The second examination timeslot will be on Monday 19.09.2022 at 9–11 in the Kleiner Hörsaal at Wegeler Str. 10.

**Some references:**

- W. Fulton and J. Harris - Representation theory: a first course (zbMATH Open link)
- J. Humphreys - Introduction to Lie algebras and representation theory (zbMATH Open link)
- A. Knapp - Lie groups beyond an introduction (zbMATH Open link)