Young tableaux, groups and representations

We learn about Young tableaux based on Chaps. 1-6 of Fulton's book. Then we study some of their applications in representation theory (Chaps. 7 & 8 in Fulton's book)

Students work in pairs with each pair preparing two seminar sessions.

Main reference

William Fulton
Young Tableaux
Cambridge University Press, 1997

available online (from inside the university network or via VPN) at
http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=570403

We read Part I (Chaps. 1-6) and Part II (Chaps. 7 & 8).

Discord

We can use this Discord-Server for continuous exchange.

Schedule

Before the first session everybody studies the section on notation and Chap. 1 on bumping and sliding. The videos on https://tinyurl.com/young-tableaux may be useful when studying Chap. 1. Solve exercises 1 & 2. If anything in Chap. 1 is unclear, discuss it on Discord before the first session.

^* additional reading: Donal E. Knuth, The Art of Computer Programming, Volume 3 Sorting and Searching, Section 5.1.4 Tableaux and Involutions, Addison-Wesley, 1973

^† additional reading: Ian G. Macdonald, Symmetric Functions and Hall Polynomials, Chapter I Symmetric Functions, Clarendon Press, 1979

How to prepare

(A) How to prepare for sessions of the other teams

• Read the chapter once, as if it was a novel, i.e., keep reading even if there's something you don't understand, but...
  ...mark or note down terms you don't know and places (in definitions, sentences, proofs, or statements in the text) in which there's something you don't understand.
• Optional: Look up unfamiliar terms.
• Optional: Formulate specific questions about the unclear passages.
• Optional: Post these questions on Discord.
• Read through all the exercises. Do you understand the task? If not, formulate a question about what is unclear.
• Optional: Work on some or all of the exercises.
• Optional: Post comments or questions about the exercises on Discord.
• Make a brief note of what you definitely want to learn in the session, e.g., formulate of a key question.

(B) How to prepare for the sessions of your team

(B1) Learning the topics of your sessions.

Study the chapter assigned to you:

• Initially, read the chapter once in the same way you would if it was not your team's session.
• Reread the chapter extracting all definitions, lemmas, propositions etc.
• Make sure you understand all statements.
• Study the proofs.
• Solve the exercises.

Discuss all statements, proofs, examples and exercises with your team partner.

If there are questions that you'd like to discuss with us, make an appointment via email, explicitly stating the problem(s) you want to discuss - the latter is an important part of your learning experience and must not be skipped.

You should have completed step (B1) two weeks before your sessions at the latest.

(B2) Preparing your sessions.

• What are the main questions / topics / theorems you will cover?
• What are good examples illustrating the main points?
• Decide which parts you want to present in which way (blackboard presentation, slides, developing something together with the audience, using a handout/worksheet, etc. - everything is allowed).
• Structure the material. What should go in which session? Who will speak at what time?
• Optional: Prepare a handout for your fellow students if you plan to actively work with it in the sessions.
• Let your fellow students know how you expect them to prepare before your sessions and, in particular, between the two sessions taught by your team (central questions to think about, little exercises, puzzles, a short text to read, a video to watch, etc.).

You should have completed step (B2) about one week before your sessions.

What else?

Contribute to the other sessions. Ask questions! Discuss!