Details of MA4202 (Spring 2014)

Level: 4 Type: Theory Credits: 3.0

Course CodeCourse NameInstructor(s)
MA4202 Representations of Groups and Algebras Mithun Mukherjee

Syllabus

  • Representations of Finite Groups : Definitions, Schurs theorem, characters, induced representation and restrictions, group algebra, representations in positive characteristic, representation of symmetric groups, Young's tableaux, character formulas, Schur functors.

  • Lie Groups and Lie Algebras : Definitions, exponential map, semi-simple Lie algebras, representations of $SL_n(\mathbb C), GL_n(\mathbb C)$, representations of $sl_2(\mathbb C).$

  • Classifications of Complex Simple Lie Algebras : The classification theorem, root system, Dynkin diagrams, associating an algebra with a diagram, classifying all simple Dynkin diagrams.

References

  1. W. Fulton and J. Harris, Representation Theory : A First Course, Graduate Texts in Mathematics, Springer-Verlag, 1989.

  2. C. Musili, Representations of finite groups, Hindustan Book Agency, 1993.

  3. W. Fulton and A. Young, Tableaux with Applications to Representation Theory and Geometry, Cambridge University Press, 1997.

Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 2 Not Allowed
2 IP 4 Core
3 MR 2 Not Allowed
4 MR 4 Not Allowed
5 MS 8 Core
6 RS 1 Not Allowed
7 RS 2 Not Allowed