MAL522 (Representation Theory of Finite Groups-27M)

Syllabus (Pg 176) 

There will be 42 lectures of 55 minutes each.

Office Hours: Appointment basis.

Evaluation Plan

• End-Semester Examination: 

• Mid-Semester Examination: 

• Quizzes: 2 quizzes, 

• Presentation: 

Tentative course plan is the following.

• Lecture 01: What are representations of finite groups and why should we study them, examples of representations.

• Lecture 02: Invariant subspaces, sub-representations, irreducible representations, direct sum, dual representation.

• Lecture : FG-Modules and their connection with representations of G over F, Permuttion Modules.

• Lecture : FG-Modules and equivalent representations, FG-sbmodules, irreducible FG-modules and representations.

• Lecture : FG-homomorphism and semisimple representations.

• Lecture : Group algebra, the regular (and faithful) FG-module.

• Lecture : Tensor product of vector spaces and representations.

• Lecture : Exterior powers of representations.

• Lecture : Symmetric powers of representations.

• Lecture : Maschke's theorem.

• Lecture : Consequences of Maschke's theorem.

• Lecture : Schur's Lemma.

• Lecture : Applications of Schur's Lemma.

• Lecture : More on group algebra.

• Lecture : Conjugacy classes and characters.

• Lecture : Examples of characters.

• Lecture : Orthogonality relations.

• Lecture : Regular representation.

• Lecture : Regular representation.

• Lecture : Number of irreducible representations.

• Lecture : Number of irreducible representations.

• Lecture : Number of irreducible representations.

• Lecture : Number of irreducible representations.

• Lecture : Character Tables.

• Lecture : Character Tables.

• Lecture : Character Tables.

• Lecture : Induced representations: Restriction of representations.

• Lecture : Induced representations.

• Lecture : Character of induced representations.

• Lecture : Character of induced representations.

• Lecture : Character of induced representations.

• Lecture : Frobenius reciprocity formula.

• Lecture : Frobenius reciprocity formula.

• Lecture : Mackey's irreducibility criterion.

• Lecture : Mackey's irreducibility criterion.

• Lecture : Representation theory of symmetric and alternating group.

• Lecture : Burnside's theorem.

• Lecture : Burnside's theorem.

• Lecture : Decoposition of group algebra.

• Lecture : Artin's theorem on induced characters.

• Lecture 41: Elementary subgroups.

• Lecture 42: Brauer's theorem.

End-semester examination