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).
https://www.isibang.ac.in/~adean/infsys/database/MMath/E5RT.html
- Teacher: Manish Kumar