Mathematics

**MTH ****410: Representation Theory**** ****(4)**

**Pre-requisites**: MTH 301, MTH 302

Representations of groups, subrepresentations, Irreducible representations, tensor product of representations, Maschke's theorem, Wedderburn decomposition

Characters of representations, Generalized characters, Schurs lemma, Orthogonality, Regular representations, Decomposition theorems

Representations of direct product of finite groups, Induced representations, Reciprocity theorem

Representations and characters of standard finite and infinite groups: cyclic groups, dihedral groups, symmetric and alternating groups of small order etc.

Applications of Representation Theory

*Suggested Books*:

- J. P. Serre,
*Linear Representations of Finite groups*(Graduate Texts in Mathematics), 2nd Edition, Springer-Verlag New York Inc., 1977 - W. Fulton and J. Harris,
*Representation Theory*,*A First Course*, 2nd Indian reprint, Springer India, 2007 *G. James, M. Liebeck, Representations and Characters of Groups*, Cambridge University Press, 2001- M. Suzuki,
*Group Theory II*, Springer-Verlag, 1983

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