| Course Archives Theoretical Statistics and Mathematics Unit | ||||||||
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Course: Representation Theory of Finite Groups Instructor: Manish Kumar Room: G25 Level: Postgraduate Time: Currently offered |
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| 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). Evaluation:
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[ Semester Schedule ][ SMU ] [Indian Statistical Institute] |