Course: Linear Representations of Finite Groups [ July 1 to July 13th, 2024]

Groups are realized as symmetries of objects such as sets, vector spaces, field extensions, geometric and combinatorial objects. In fact, they mostly occur as realizations and hence their ubiquity and utility. The earliest study of such representation was on sets (permutation groups), and the representation as vector space isomorphisms (Linear representations).

Instructor: N.S. Narasimha Sastry

Topics: Definition of linear representation of a group, many examples, sums and products of representations, irreducible and indecomposable representations, Maschke's theorem, Schur's lemma, character of a representation, orthogonality relations. Induced representations and Frobenius reciprocity may also be covered.

Background required: Those who have a good background in Group theory (M.Sc. first year level minimum) and linear algebra, will be able to follow these lectures. PhD Scholars and young faculty members are also eligible to apply.

Selected candidates are listed below.