Spring 2016 : MA 5017 Homepage
(Representation Theory M.Sc. II elective)



This was an elective course for students in the final year of their masters degree course and was also open for Ph.D. students. Since this was the first time the course was taught in IITM, it was an amalgamation of various topics. Initially, we followed the book Linear representations of finite groups by Serre. Subsequently, we studied Young tableaux and representations of for which We referred to Representation theory : A first course by Fulton and Harris and Representation Theory of finite groups by Steinberg. Finally we gave a very brief introduction to the representation theory of compact groups (with some vague remarks about Lie groups).

Concepts which were taught included various operations on representations, the averaging trick, Schur's lemma, studying representations via their characters (irreducible representations, orthogonality of their characters, the regular representation, irreducible representations and conjugacy classes, uniqueness of isotypic components and the canonical decomposition), integrality properties of characters, induced representations, Frobenius reciprocity, Mackey's irreducibility criterion, Young tableaux and Sprecht representations. Brief ideas about compact (Lie) groups and the Haar measure on these was also discussed.

The scoring was based on 2 quizzes worth 22 points each, 6 homeworks totalling 14 points and a comprehensive final.

The class was credited by 9 students including 1 Ph.D. student, but there were about an equal number of students of varying backgrounds who chose to sit in for classes.


     

     

Thank you to everyone who participated.

     

     


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