Course Archives Theoretical Statistics and Mathematics Unit

Course: Representation Theory of Finite Groups Level: Postgraduate Time: Currently not offered

Syllabus Past Exams Syllabus: i) Representation of finite groups - definition and examples; symmetric and exte rior powers; group algebra, Maschkes Theorem, Simple Modules over group algebras. ii) Characters and Orthogonality relations; Fourier analysis on finite Abelian groups; Burnsides pq theorem. Construction of character tables with examples. iii) Permutation representations; Induced representations; Frobenius reciprocity; iv) Representation theory of symmetric groups - partitions and tableau, Young diagrams and Frobenius character formula (from Fulton-Harris). v) Time permitting: Brauers theorem on induced characters. Suggested Texts : (a) Benjamin Steinberg, Representation theory of finite groups, Springer (2012). (b) E. Kowalski, An Introduction to the Representation Theory of Groups, AMS (2014). (c) W. Fulton And J. Harris, Representation Theory, A first course; GTM 129 Springer (1991). (d) C.W. Curtis and I. Reiner, Representation Theory of finite Groups and Associa- tive Algebras, Springer. (e) J-P Serre, Linear Representations of Finite Groups; GTM 42 Springer (2012). (f) N. Jacobson, Basic Algebra II, W.H. Freeman and Co (1985). Top of the page Past Exams

Midterm 25.pdf Semestral 25.pdf Supplementary and Back Paper 25.pdf Top of the page

[ Semester Schedule ][ SMU ] [Indian Statistical Institute]