Lecture 1 - Basics of vector spaces
Lecture 2 - Inner product spaces
Lecture 3 - Diagonalization
Lecture 4 - Generalized eigen spaces
Lecture 5 - Decomposition theorems
Lecture 6 - Definition of representation
Lecture 7 - Isomorphism theorems
Lecture 8 - Indecomposable representations
Lecture 9 - Schur's Lemma
Lecture 10 - Filtration of representations
Lecture 11 - Construction of new representations by extensions
Lecture 12 - Basics of representation theory of finite groups
Lecture 13 - Classification of irreducible representations of finite cyclic group and Symmteric group
Lecture 14 - Irreducibility via Cyclic Vectors
Lecture 15 - Construction of representations of group generated by a set with defining relations
Lecture 16 - Complete reducibility of unitary representations
Lecture 17 - Complete reducibility of finite dimensional representations of finite groups
Lecture 18 - Projection map from representation of G to its fixed subspace
Lecture 19 - Character Theory: Basic properties
Lecture 20 - Orthogonality relations of irreducible characters of finite group
Lecture 21 - Orthonormal subset of space of class functions and Orthogonality of irreducible characters
Lecture 22 - Schur's orthogonality relations and its applications
Lecture 23 - Applications of character theory
Lecture 24 - Regular representation, decomposition of regular representation
Lecture 25 - Orthonormal basis of space of class functions and computation of character tables
Lecture 26 - Orthogonality of the columns of the character table
Lecture 27 - Representations of finite abeilian group
Lecture 28 - Algebraic numbers and equivalent conditions for algebraic integers
Lecture 29 - Dimension theorem
Lecture 30 - Applications of dimension theorem
Lecture 31 - Character table computation of groups: Q_8, D_8, A_4
Lecture 32 - Burnside Theorem and its proof
Lecture 33 - Proof of key result used in Burnside Theorem
Lecture 34 - Notion of Tensor product
Lecture 35 - Basic properties of Tensor product
Lecture 36 - Symmetric tensor product
Lecture 37 - Alternating tensor product
Lecture 38 - G-action on Symmetric and exterior tensor product
Lecture 39 - Graded character of Symmetric tensor algebra and exterior algebra
Lecture 40 - Alternate proof of orthogonality of irreducible characters
Lecture 41 - Density theorem
Lecture 42 - Frobenius theorem
Lecture 43 - Induced representation
Lecture 44 - Frobenius reciprocity
Lecture 45 - Mackey's restrcition formula
Lecture 46 - Mackey's irreducibility criterion
Lecture 47 - Fourier analysis on finite groups
Lecture 48 - Fourier inversion
Lecture 49 - Fourier analysis on nonabeilian groups
Lecture 50 - Applications of Fourier analysis on finite groups
Lecture 51 - Cayley graph and its eigenvalues
Lecture 52 - Notations and combinatorics in representation theory of symmetric group
Lecture 53 - Irreducible representations of symmetric group
Lecture 54 - Permutation modules
Lecture 55 - Constructing irreducibles of symmetric group
Lecture 56 - Classification of irreducible representations of symmetric group
