Course Details
Subject {L-T-P / C} : MA5117 : Representation Theory { 3-0-0 / 3}
Subject Nature : Theory
Coordinator : Dr. Bikramaditya Sahu
Syllabus
Group representations, Maschke’s theorem and completely reducibility, Characters, Inner product of Characters, Orthogonality relations, Burnside’s theorem, induced characters, Frobenius reciprocity, induced representations, Mackey’s Irreducibility Criterion, Character table of some well-known groups, Representation theory of the symmetric group: partitions and tableaux, constructing the irreducible representations.
Course Objectives
- To give an introduction to representation theory of finite groups.
- To give a relation between linear algebra and group theory.
- To study properties of certain group of by looking at the corresponding representation.
- To understand Burnside's theorem.
Course Outcomes
Students will learn basics on representation theory of finite groups. This course will give an idea how representation theory is useful in different areas of Mathematics as well as Physics. This course will help them to explore research on Representation Theory of finite groups and related areas.
Essential Reading
- William Fulton and Harris Joe, Representation Theory: A First Course., Springer, 2004
- G. James, M. Liebeck, Representations and Characters of Groups, Cambridge University Press, 2010.
Supplementary Reading
- J-P. Serre, Linear Representations of Finite Groups, Graduate Texts in Mathematics 42, Springer-Verlag, 1977.
- Benjamin Steinberg, Representation Theory of Finite Groups: An Introductory Approach, Universitext, Springer, 2012.