Course - Introduction to Representation Theory of Finite Groups

Instructor

Wei-Liang Sun

Scope

Representation theory of finite groups is one of the important theories in mathematical branches. It concerns the study of abstract finite groups by using concrete matrices. In this seminar, we provide basic notions of this theory. It will be suitable for students who have taken undergraduate courses involving group theory and linear algebra.

Book

Representations and Characters of Groups by Gordon James and Martin Liebeck.

The Symmetric Group by Bruce E. Sagan.

Schedule

We follow the regular venue and time below; if there is any change, it will be annotated in the schedule. n

Venue: SC4011-2

Time: Thursday 11:10 ~ 12:00

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[Note]

  1. 2/25, Introduction to Representation Theory of Finite Groups [ abstract ]

  2. 3/4, Equivalent Representations and Characters [ abstract ]

  3. 3/11, A Power of Characters [ abstract ]

  4. 3/18, Examples for Representations of Nonabelian Groups [ abstract ]

  5. 3/25, Reducibility of Representations [ abstract ]

  6. 4/1, Irreducible Representations [abstract]

  7. 4/8, Schur's Lemma [abstract]

  8. 4/15, The Regular Representation [abstract]

  9. 4/22, Conjugacy Classes and The Character Table [abstract]

  10. 4/29, Inner Product and Orthogonality Relations [abstract]

  11. 5/6, Symmetric Groups [abstract]

  12. 5/13, Young Tableaux [abstract]

  13. 5/20, Specht Modules [abstract]

  14. 5/27, Bases of Specht Modules [abstract]

  15. 6/3, Standard Young Tableaux [abstract]

  16. 6/10, Hook Length Formula [abstract]

  17. 6/17, The Largest Degree [abstract]

  18. 6/24, The RS Algorithm [abstract]

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