Lecture 1 - Basic Theory of Lie algebras Lecture 2 - Basic Theory of Lie algebras (Continued...) Lecture 3 - Basic Theory of Lie algebras (Continued...) Lecture 4 - Representation Theory of Lie algebras Lecture 5 - Representation Theory of Lie algebras (Continued...) Lecture 6 - Representation of Lie algebras Lecture 7 - Classification of 2 dimensional representation of two dimensional non-abelian Lie algebra Lecture 8 - Isomorphism Theorem Lecture 9 - Characterization of completely reducible module Lecture 10 - Representation theory of sl2(C) Lecture 11 - Irreducible representation of sl2(C) Lecture 12 - Irreducible representation of sl2(C) (Continued...) Lecture 13 - Complete reducibility of sl2(C) Lecture 14 - Complete reducibility of sl2(C) (Continued...) Lecture 15 - Representation theory of sl2(C)-basic observation Lecture 16 - Application of sl2(C) representation theory in combinatorics Lecture 17 - Constructions of new representations Lecture 18 - Construction of universal algebras - I Lecture 19 - Construction of universal algebras - II Lecture 20 - Non-degenerate and invariant bilinear forms Lecture 21 - Schur’s lemma and Killing form Lecture 22 - Killing form of general and special linear Lie algebras Lecture 23 - The universal enveloping algebra Lecture 24 - Properties of the universal enveloping algebra Lecture 25 - The Casimir operator for representations of gln(C) and sln(C) Lecture 26 - Weyl’s theorem of complete reducibility Lecture 27 - The structure of sln+1(C) Lecture 28 - Representations of sln+1(C) - I Lecture 29 - Representations of sln+1(C) - II Lecture 30 - Representations of sln+1(C) - III Lecture 31 - Casimir operator and highest weight modules - I Lecture 32 - Casimir operator and highest weight modules - II Lecture 33 - Irreducible representations of sln+1(C) Lecture 34 - Verma module and its irreducible quotient Lecture 35 - Verma modules and standard cyclic irreducible modules Lecture 36 - Finite dimensional standard cyclic irreducible modules Lecture 37 - Standard cyclic irreducible modules Lecture 38 - Character Theory - I Lecture 39 - Character Theory - II Lecture 40 - Deniminator Identity - Prep 1 Lecture 41 - Deniminator Identity - Prep 2 Lecture 42 - Proof of the denominator identity Lecture 43 - Freudenthal's formula Lecture 44 - The Weyl character formula Lecture 45 - The Laplacian operator and the Weyl Character Formula Lecture 46 - Proof of the Weyl Character Formula Lecture 47 - Applications of Weyl Character formula Lecture 48 - The Weyl dimension formula, Schur polynomials Lecture 49 - Semi-standard Young Tableaux Lecture 50 - BGG resolution