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.
Representations and Characters of Groups by Gordon James and Martin Liebeck.
The Symmetric Group by Bruce E. Sagan.
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]
2/25, Introduction to Representation Theory of Finite Groups [ abstract ]
3/4, Equivalent Representations and Characters [ abstract ]
3/11, A Power of Characters [ abstract ]
3/18, Examples for Representations of Nonabelian Groups [ abstract ]
3/25, Reducibility of Representations [ abstract ]
4/1, Irreducible Representations [abstract]
4/8, Schur's Lemma [abstract]
4/15, The Regular Representation [abstract]
4/22, Conjugacy Classes and The Character Table [abstract]
4/29, Inner Product and Orthogonality Relations [abstract]
5/6, Symmetric Groups [abstract]
5/13, Young Tableaux [abstract]
5/20, Specht Modules [abstract]
5/27, Bases of Specht Modules [abstract]
6/3, Standard Young Tableaux [abstract]
6/10, Hook Length Formula [abstract]
6/17, The Largest Degree [abstract]
6/24, The RS Algorithm [abstract]
Representation Theory of Finite Groups and Finite-Dimensional Algebras, edited by G. O. Michler and C. M. Ringel.
Representations of finite groups and applications, lectured by Pham Huu Tiep at ICM 2018.
Group Representations in Probability and Statistics by Persi Diaconis.
The Representation Theory of the Symmetric Group by Gordon James and Adalbert Kerber.
Young Tableaux by William Fulton.